JEE MAIN

<div><div><li> <p>The correct truth table for the following logic circuit is:</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/e3c61c7f-b90d-45b7-b45c-37791896a81c.jpg" style="width:2.82945in;height:0.90986in" alt=""> </p></div>

<div><p>Using Boolean algebra and DeMorgan theorem, Output</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      Y 
    </mi> 
    <mo>
      = 
    </mo> 
    <mover> 
     <mi>
       A 
     </mi> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      + 
    </mo> 
    <mi>
      A 
    </mi> 
    <mo>
      ⋅ 
    </mo> 
    <mi>
      B 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     Y = \overline{A} + A \cdot B 
   </annotation> 
  </semantics> 
 </math> </p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/6d203439-f20b-4a63-9798-3ee483fe81b8.jpg" style="width:0.97359in;height:1.60048in" alt=""> </p></div>

<div><div><li> <p>The truth table for the circuit given below is:</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/a3e70a31-d8c5-4cda-8168-ecb85e70241d.jpg" style="width:3.01365in;height:1.11474in" alt=""> </p></div>

<div><p>Using Boolean algebra and DeMorgan theorem, Output</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      Z 
    </mi> 
    <mo>
      = 
    </mo> 
    <mi>
      A 
    </mi> 
    <mo>
      ⋅ 
    </mo> 
    <mover> 
     <mi>
       B 
     </mi> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      + 
    </mo> 
    <mover> 
     <mi>
       A 
     </mi> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      ⋅ 
    </mo> 
    <mi>
      B 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     Z = A \cdot \overline{B} + \overline{A} \cdot B 
   </annotation> 
  </semantics> 
 </math> </p><p>Thus equivalent circuit is XOR Gate</p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/eb4ad623-21a4-4328-ac33-7757fae5356a.jpg" style="width:3.22982in;height:1.02409in" alt=""> </p><p style="text-align:left;"> 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      T 
    </mi> 
    <mi>
      r 
    </mi> 
    <mi>
      u 
    </mi> 
    <mi>
      t 
    </mi> 
    <mi>
      h 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      t 
    </mi> 
    <mi>
      a 
    </mi> 
    <mi>
      b 
    </mi> 
    <mi>
      l 
    </mi> 
    <mi>
      e 
    </mi> 
    <mo>
      : 
    </mo> 
   </mrow> 
   <annotation encoding="application/x-tex">
     Truth\ table: 
   </annotation> 
  </semantics> 
 </math> </p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/b6e5a435-cafa-4734-b955-17faf8abdec2.jpg" style="width:0.83676in;height:1.24623in" alt=""> </p></div>

<div><div><li> <p>Which of the following circuits is reverse-biased?</p> </li></div></div>

<div><p>For a diode to be reverse biased, The P-end is connected to the negative terminal of the battery</p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/c3fa6356-c0e9-4cee-83aa-af652f77ce20.jpg" style="width:1.54683in;height:0.4194in" alt=""> </p><p>Is reversed biased</p></div>

<div><div><li> <p>For the circuit shown above, equivalent GATE is:</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/797a3b8f-757a-4ca2-8bda-9d7e36ce2f37.jpg" style="width:2.394in;height:0.9765in" alt=""> </p></div>

<div><p>Using Boolean algebra and DeMorgan theorem, Output:</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      Y 
    </mi> 
    <mo>
      = 
    </mo> 
    <mover> 
     <mrow> 
      <mrow> 
       <mo stretchy="true" form="prefix">
         ( 
       </mo> 
       <mover> 
        <mrow> 
         <mi>
           A 
         </mi> 
         <mo>
           ⋅ 
         </mo> 
         <mi>
           B 
         </mi> 
        </mrow> 
        <mo accent="true">
          ¯ 
        </mo> 
       </mover> 
       <mo stretchy="true" form="postfix">
         ) 
       </mo> 
      </mrow> 
      <mo>
        ⋅ 
      </mo> 
      <mrow> 
       <mo stretchy="true" form="prefix">
         ( 
       </mo> 
       <mover> 
        <mrow> 
         <mi>
           A 
         </mi> 
         <mo>
           + 
         </mo> 
         <mi>
           B 
         </mi> 
        </mrow> 
        <mo accent="true">
          ¯ 
        </mo> 
       </mover> 
       <mo stretchy="true" form="postfix">
         ) 
       </mo> 
      </mrow> 
     </mrow> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      = 
    </mo> 
    <mover> 
     <mover> 
      <mrow> 
       <mi>
         A 
       </mi> 
       <mo>
         ⋅ 
       </mo> 
       <mi>
         B 
       </mi> 
      </mrow> 
      <mo accent="true">
        ¯ 
      </mo> 
     </mover> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      + 
    </mo> 
    <mspace width="0.222em"></mspace> 
    <mover> 
     <mover> 
      <mrow> 
       <mi>
         A 
       </mi> 
       <mo>
         + 
       </mo> 
       <mi>
         B 
       </mi> 
      </mrow> 
      <mo accent="true">
        ¯ 
      </mo> 
     </mover> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
   </mrow> 
   <annotation encoding="application/x-tex">
     Y = \overline{\left( \overline{A \cdot B} \right) \cdot \left( \overline{A + B} \right)} = \overline{\overline{A \cdot B}} + \ \overline{\overline{A + B}} 
   </annotation> 
  </semantics> 
 </math> </p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      Y 
    </mi> 
    <mo>
      = 
    </mo> 
    <mi>
      A 
    </mi> 
    <mo>
      ⋅ 
    </mo> 
    <mi>
      B 
    </mi> 
    <mo>
      + 
    </mo> 
    <mi>
      A 
    </mi> 
    <mo>
      ⋅ 
    </mo> 
    <mi>
      B 
    </mi> 
    <mo>
      = 
    </mo> 
    <mi>
      A 
    </mi> 
    <mrow> 
     <mo stretchy="true" form="prefix">
       ( 
     </mo> 
     <mi>
       B 
     </mi> 
     <mo>
       + 
     </mo> 
     <mn>
       1 
     </mn> 
     <mo stretchy="true" form="postfix">
       ) 
     </mo> 
    </mrow> 
    <mo>
      + 
    </mo> 
    <mi>
      B 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     Y = A \cdot B + A \cdot B = A(B + 1) + B 
   </annotation> 
  </semantics> 
 </math> </p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      Y 
    </mi> 
    <mo>
      = 
    </mo> 
    <mi>
      A 
    </mi> 
    <mo>
      + 
    </mo> 
    <mi>
      B 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     Y = A + B 
   </annotation> 
  </semantics> 
 </math>Thus the equivalent circuit is OR Gate</p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/a953bb44-367a-4bb4-958c-a7bbdfcddbf7.jpg" style="width:2.40931in;height:0.92182in" alt=""> </p></div>

<div><div><li> <p>In the given circuit, the voltage across load resistance (R<sub>L</sub>) is:</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/1b29b423-0fde-4bdc-a99a-56e291f5cc34.jpg" style="width:2.02783in;height:0.86907in" alt=""> </p></div>

<div><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      S 
    </mi> 
    <mi>
      i 
    </mi> 
    <mi>
      n 
    </mi> 
    <mi>
      c 
    </mi> 
    <mi>
      e 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      t 
    </mi> 
    <mi>
      h 
    </mi> 
    <mi>
      e 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      d 
    </mi> 
    <mi>
      i 
    </mi> 
    <mi>
      o 
    </mi> 
    <mi>
      d 
    </mi> 
    <mi>
      e 
    </mi> 
    <mi>
      s 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      a 
    </mi> 
    <mi>
      r 
    </mi> 
    <mi>
      e 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      S 
    </mi> 
    <mi>
      i 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      a 
    </mi> 
    <mi>
      n 
    </mi> 
    <mi>
      d 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      G 
    </mi> 
    <mi>
      e 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      b 
    </mi> 
    <mi>
      a 
    </mi> 
    <mi>
      s 
    </mi> 
    <mi>
      e 
    </mi> 
    <mi>
      d 
    </mi> 
    <mo>
      : 
    </mo> 
   </mrow> 
   <annotation encoding="application/x-tex">
     Since\ the\ diodes\ are\ Si\ and\ Ge\ based: 
   </annotation> 
  </semantics> 
 </math> </p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      F 
    </mi> 
    <mi>
      o 
    </mi> 
    <mi>
      r 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      S 
    </mi> 
    <mi>
      i 
    </mi> 
    <mo>
      : 
    </mo> 
    <mspace width="0.222em"></mspace> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       B 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      0.7 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     For\ Si:\ V_{B} = 0.7\text{\ }V 
   </annotation> 
  </semantics> 
 </math> </p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      F 
    </mi> 
    <mi>
      o 
    </mi> 
    <mi>
      r 
    </mi> 
    <mspace width="0.222em"></mspace> 
    <mi>
      G 
    </mi> 
    <mi>
      e 
    </mi> 
    <mo>
      : 
    </mo> 
    <mspace width="0.222em"></mspace> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       B 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      0.3 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     For\ Ge:\ V_{B} = 0.3\text{\ }V 
   </annotation> 
  </semantics> 
 </math> </p><p>Voltage drop across both diode</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      0.7 
    </mn> 
    <mo>
      + 
    </mo> 
    <mn>
      0.3 
    </mn> 
    <mo>
      = 
    </mo> 
    <mn>
      1 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{1} = 0.7 + 0.3 = 1\text{\ }V 
   </annotation> 
  </semantics> 
 </math> </p><p>So remaining 14 volt will drop across 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <msub> 
    <mi>
      R 
    </mi> 
    <mi>
      L 
    </mi> 
   </msub> 
   <annotation encoding="application/x-tex">
     R_{L} 
   </annotation> 
  </semantics> 
 </math></p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       R 
     </mi> 
     <mrow> 
      <mi>
        e 
      </mi> 
      <mi>
        q 
      </mi> 
     </mrow> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      1.5 
    </mn> 
    <mo>
      + 
    </mo> 
    <mn>
      2.5 
    </mn> 
    <mo>
      = 
    </mo> 
    <mn>
      4 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      k 
    </mi> 
    <mi>
      Ω 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     R_{eq} = 1.5 + 2.5 = 4\ k\Omega 
   </annotation> 
  </semantics> 
 </math> </p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       L 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mi>
      i 
    </mi> 
    <mi>
      R 
    </mi> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mn>
       14 
     </mn> 
     <mrow> 
      <mn>
        4 
      </mn> 
      <mspace width="0.222em"></mspace> 
      <mi>
        k 
      </mi> 
      <mi>
        Ω 
      </mi> 
     </mrow> 
    </mfrac> 
    <mo>
      × 
    </mo> 
    <mn>
      2.5 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      k 
    </mi> 
    <mi>
      Ω 
    </mi> 
    <mo>
      = 
    </mo> 
    <mn>
      8.75 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{L} = iR = \frac{14}{4\ k\Omega} \times 2.5\ k\Omega = 8.75\ V 
   </annotation> 
  </semantics> 
 </math> </p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/98e559e6-99f9-4a54-8108-359cc300ed2c.jpg" style="width:1.85561in;height:0.91338in" alt=""> </p></div>

<div><div><li> <p>The reverse break-down voltage of a Zener diode is 5.6 V in the given circuit. The current I<sub>z</sub> through the Zener is</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/d375b1a7-1f38-468b-8367-d3601d7718af.jpg" style="width:2.04427in;height:0.9387in" alt=""> </p></div>

<div><p>Given: reverse breakdown voltage of a Zener diode connected in the circuit is 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       Z 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      5.6 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{Z} = 5.6\text{\ }V 
   </annotation> 
  </semantics> 
 </math></p><p>To find: The current 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <msub> 
    <mi>
      I 
    </mi> 
    <mi>
      Z 
    </mi> 
   </msub> 
   <annotation encoding="application/x-tex">
     I_{Z} 
   </annotation> 
  </semantics> 
 </math> through the zener diode.</p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/1e2dd069-9760-4601-88d3-4b8e5b795003.jpg" style="width:2.5222in;height:1.05471in" alt=""> </p><p>Voltage drop cross the Zener diode: 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       Z 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      5.6 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{Z} = 5.6\text{\ }V 
   </annotation> 
  </semantics> 
 </math></p><p>Voltage drop across the 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       R 
     </mi> 
     <mn>
       2 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      800 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      Ω 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     R_{2} = 800\ \Omega 
   </annotation> 
  </semantics> 
 </math> resistor: 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       Z 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      5.6 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{Z} = 5.6\text{\ }V 
   </annotation> 
  </semantics> 
 </math></p><p>Current through the 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       R 
     </mi> 
     <mn>
       2 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      800 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      Ω 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     R_{2} = 800\ \Omega 
   </annotation> 
  </semantics> 
 </math> resistor:</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       I 
     </mi> 
     <mn>
       2 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <msub> 
      <mi>
        V 
      </mi> 
      <mi>
        Z 
      </mi> 
     </msub> 
     <msub> 
      <mi>
        R 
      </mi> 
      <mn>
        2 
      </mn> 
     </msub> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mn>
       5.6 
     </mn> 
     <mn>
       800 
     </mn> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mn>
      7 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      m 
    </mi> 
    <mi>
      A 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     I_{2} = \frac{V_{Z}}{R_{2}} = \frac{5.6}{800} = 7\text{\ }mA 
   </annotation> 
  </semantics> 
 </math> </p><p>Voltage drop across the 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       R 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      200 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      Ω 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     R_{1} = 200\ \Omega 
   </annotation> 
  </semantics> 
 </math> resistor:</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mi>
      V 
    </mi> 
    <mo>
      − 
    </mo> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       Z 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      9 
    </mn> 
    <mo>
      − 
    </mo> 
    <mn>
      5.6 
    </mn> 
    <mo>
      = 
    </mo> 
    <mn>
      3.4 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{1} = V - V_{Z} = 9 - 5.6 = 3.4\text{\ }V 
   </annotation> 
  </semantics> 
 </math> </p><p>Current through the 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       R 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      200 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      Ω 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     R_{1} = 200\ \Omega 
   </annotation> 
  </semantics> 
 </math> resistor:</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       I 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <msub> 
      <mi>
        V 
      </mi> 
      <mn>
        1 
      </mn> 
     </msub> 
     <msub> 
      <mi>
        R 
      </mi> 
      <mn>
        1 
      </mn> 
     </msub> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mn>
       3.4 
     </mn> 
     <mn>
       200 
     </mn> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mn>
      17 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      m 
    </mi> 
    <mi>
      A 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     I_{1} = \frac{V_{1}}{R_{1}} = \frac{3.4}{200} = 17\text{\ }mA 
   </annotation> 
  </semantics> 
 </math> </p><p>Current 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <msub> 
    <mi>
      I 
    </mi> 
    <mi>
      Z 
    </mi> 
   </msub> 
   <annotation encoding="application/x-tex">
     I_{Z} 
   </annotation> 
  </semantics> 
 </math> through the Zener diode:</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       I 
     </mi> 
     <mi>
       Z 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <msub> 
     <mi>
       I 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      − 
    </mo> 
    <msub> 
     <mi>
       I 
     </mi> 
     <mn>
       2 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      17 
    </mn> 
    <mo>
      − 
    </mo> 
    <mn>
      7 
    </mn> 
    <mo>
      = 
    </mo> 
    <mn>
      10 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      m 
    </mi> 
    <mi>
      A 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     I_{Z} = I_{1} - I_{2} = 17 - 7 = 10\text{\ }mA 
   </annotation> 
  </semantics> 
 </math> </p></div>

<div><div><li> <p>Identify the logic operation performed by the given circuit.</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/2975de68-7a80-4ff8-9372-48a18796f16d.jpg" style="width:1.90324in;height:0.60988in" alt=""> </p></div>

<div><p>Using Boolean algebra and DeMorgan theorem, Output</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      Y 
    </mi> 
    <mo>
      = 
    </mo> 
    <mover> 
     <mi>
       A 
     </mi> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      + 
    </mo> 
    <mover> 
     <mi>
       B 
     </mi> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      = 
    </mo> 
    <mi>
      A 
    </mi> 
    <mo>
      ⋅ 
    </mo> 
    <mi>
      B 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     Y = \overline{A} + \overline{B} = A \cdot B 
   </annotation> 
  </semantics> 
 </math> </p><p>Thus the logic operation of circuit is OR gate</p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/6edb2ce0-28d0-44be-bbbe-96b00d94e964.jpg" style="width:0.89457in;height:1.37398in" alt=""> </p></div>

<div><div><li> <p>For the logic circuit shown, the output waveform at Y is:</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/012cfa18-55d4-4644-b894-fd25324bee8a.jpg" style="width:1.67852in;height:0.86193in" alt=""> </p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/4e319eb2-eeef-4253-a233-59c2106e1c29.jpg" style="width:1.66176in;height:1.18268in" alt=""> </p></div>

<div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/1b29ebb5-6172-4b9b-b528-a2c48998c74e.jpg" style="width:2.07571in;height:0.97974in" alt=""> </p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      y 
    </mi> 
    <mo>
      = 
    </mo> 
    <mover> 
     <mrow> 
      <mover> 
       <mi>
         A 
       </mi> 
       <mo accent="true">
         ‾ 
       </mo> 
      </mover> 
      <mo>
        ⋅ 
      </mo> 
      <mover> 
       <mi>
         B 
       </mi> 
       <mo accent="true">
         ¯ 
       </mo> 
      </mover> 
     </mrow> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      = 
    </mo> 
    <mover> 
     <mover> 
      <mi>
        A 
      </mi> 
      <mo accent="true">
        ¯ 
      </mo> 
     </mover> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      + 
    </mo> 
    <mover> 
     <mover> 
      <mi>
        B 
      </mi> 
      <mo accent="true">
        ¯ 
      </mo> 
     </mover> 
     <mo accent="true">
       ¯ 
     </mo> 
    </mover> 
    <mo>
      = 
    </mo> 
    <mi>
      A 
    </mi> 
    <mo>
      + 
    </mo> 
    <mi>
      B 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     y = \overline{\bar{A} \cdot \overline{B}} = \overline{\overline{A}} + \overline{\overline{B}} = A + B 
   </annotation> 
  </semantics> 
 </math> </p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/d3d7baa6-8cbc-417e-a47e-1cb9e81dfa82.jpg" style="width:2.05in;height:1.39107in" alt=""> </p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/f2766542-4222-493b-b840-a0b6700f5feb.jpg" style="width:1.54825in;height:1.35074in" alt=""> </p><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/347bee73-f2bd-4362-aaac-b9baca6d49bf.jpg" style="width:2.26417in;height:0.80036in" alt=""> </p></div>

<div><div><li> <p>Two Zener diodes (A and B) having breakdown voltages of 6V and 4V respectively, are connected as shown in the circuit. The output voltage V<sub>0</sub> variation with input voltage linearly increasing with time, is given by (V<sub>input</sub> = 0 V at t = 0) (figures are qualitative)</p> </li></div><p> <img src="http://test-master-question-data.s3.ap-south-1.amazonaws.com/questionImg/c9178a88-9639-4844-885b-c1ff7a06f57f.jpg" style="width:2.28992in;height:0.79245in" alt=""> </p></div>

<div><p>Given: Breakdown voltage for Zener diode-1 is 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      6 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{1} = 6\text{\ }V 
   </annotation> 
  </semantics> 
 </math>,</p><p>breakdown voltage for Zener diode-2 is 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <msub> 
    <mi>
      V 
    </mi> 
    <mn>
      2 
    </mn> 
   </msub> 
   <annotation encoding="application/x-tex">
     V_{2} 
   </annotation> 
  </semantics> 
 </math> 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mo>
      = 
    </mo> 
    <mn>
      4 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     = 4\text{\ }V 
   </annotation> 
  </semantics> 
 </math>,</p><p>the input voltage 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mrow> 
      <mi>
        i 
      </mi> 
      <mi>
        n 
      </mi> 
     </mrow> 
    </msub> 
    <mrow> 
     <mo stretchy="true" form="prefix">
       ( 
     </mo> 
     <mi>
       t 
     </mi> 
     <mo stretchy="true" form="postfix">
       ) 
     </mo> 
    </mrow> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{in}(t) 
   </annotation> 
  </semantics> 
 </math> varies linearly with time, at 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      t 
    </mi> 
    <mo>
      = 
    </mo> 
    <mn>
      0 
    </mn> 
    <mo>
      , 
    </mo> 
    <msub> 
     <mrow> 
      <mrow> 
       <mspace width="0.333em"></mspace> 
       <mtext mathvariant="normal"></mtext> 
       <mspace width="0.333em"></mspace> 
      </mrow> 
      <mi>
        V 
      </mi> 
     </mrow> 
     <mrow> 
      <mi>
        i 
      </mi> 
      <mi>
        n 
      </mi> 
     </mrow> 
    </msub> 
    <mrow> 
     <mo stretchy="true" form="prefix">
       ( 
     </mo> 
     <mi>
       t 
     </mi> 
     <mo stretchy="true" form="postfix">
       ) 
     </mo> 
    </mrow> 
    <mo>
      = 
    </mo> 
    <mn>
      0 
    </mn> 
   </mrow> 
   <annotation encoding="application/x-tex">
     t = 0,{\text{\ }V}_{in}(t) = 0 
   </annotation> 
  </semantics> 
 </math>.</p><p>To find: 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       o 
     </mi> 
    </msub> 
    <mrow> 
     <mo stretchy="true" form="prefix">
       ( 
     </mo> 
     <mi>
       t 
     </mi> 
     <mo stretchy="true" form="postfix">
       ) 
     </mo> 
    </mrow> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{o}(t) 
   </annotation> 
  </semantics> 
 </math> the output voltage as function of time.</p><p>For 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mtext mathvariant="normal">
       in&nbsp; 
     </mtext> 
    </msub> 
    <mo>
      &lt; 
    </mo> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mn>
       2 
     </mn> 
    </msub> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{\text{in~}} &lt; V_{2} 
   </annotation> 
  </semantics> 
 </math>, the output voltage simply follows the input voltage, that is 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mi>
       o 
     </mi> 
    </msub> 
    <mrow> 
     <mo stretchy="true" form="prefix">
       ( 
     </mo> 
     <mi>
       t 
     </mi> 
     <mo stretchy="true" form="postfix">
       ) 
     </mo> 
    </mrow> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{o}(t) 
   </annotation> 
  </semantics> 
 </math> varies linearly with time.</p><p>For 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
    <mo>
      &gt; 
    </mo> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mrow> 
      <mi>
        i 
      </mi> 
      <mi>
        n 
      </mi> 
     </mrow> 
    </msub> 
    <mo>
      &gt; 
    </mo> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mn>
       2 
     </mn> 
    </msub> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{1} &gt; V_{in} &gt; V_{2} 
   </annotation> 
  </semantics> 
 </math>: Zener diode-2 is in breakdown region, so we see a change in slope of the output voltage.</p><p>For 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mtext mathvariant="normal">
       in&nbsp; 
     </mtext> 
    </msub> 
    <mo>
      &gt; 
    </mo> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mn>
       1 
     </mn> 
    </msub> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{\text{in~}} &gt; V_{1} 
   </annotation> 
  </semantics> 
 </math>: Zener diode- 1 is also in breakdown region, so we see a constant output voltage independent of time.</p></div>

<div><div><li> <p>An NPN transistor is used in common emitter configuration as an amplifier with 1 kΩ load resistance. Signal voltage of 10mV is applied across the base-emitter. This produces a 3 mA change in the collector current and 15 μA change in the base current of the amplifier. The input resistance and voltage gain are</p> </li></div></div>

<div><p>Given: An NPN transistor is used in a common emitter configuration as an amplifier,</p><p>load resistance is 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       R 
     </mi> 
     <mi>
       L 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      1 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      k 
    </mi> 
    <mi>
      Ω 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     R_{L} = 1\ k\Omega 
   </annotation> 
  </semantics> 
 </math>,</p><p>signal voltage applied across the base-emitter is 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       V 
     </mi> 
     <mtext mathvariant="normal">
       in&nbsp; 
     </mtext> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      10 
    </mn> 
    <mspace width="0.222em"></mspace> 
    <mi>
      m 
    </mi> 
    <mi>
      V 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     V_{\text{in~}} = 10\ mV 
   </annotation> 
  </semantics> 
 </math>,</p><p>change in collector current due to the signal voltage is 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      Δ 
    </mi> 
    <msub> 
     <mi>
       I 
     </mi> 
     <mi>
       C 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      3 
    </mn> 
    <mrow> 
     <mspace width="0.333em"></mspace> 
     <mtext mathvariant="normal"></mtext> 
     <mspace width="0.333em"></mspace> 
    </mrow> 
    <mi>
      m 
    </mi> 
    <mi>
      A 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     \Delta I_{C} = 3\text{\ }mA 
   </annotation> 
  </semantics> 
 </math>,</p><p>change in base current due to the signal voltage is 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      Δ 
    </mi> 
    <msub> 
     <mi>
       I 
     </mi> 
     <mi>
       B 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mn>
      15 
    </mn> 
    <mi>
      μ 
    </mi> 
    <mi>
      A 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     \Delta I_{B} = 15\mu A 
   </annotation> 
  </semantics> 
 </math>.</p><p>To find: The input resistance 
 <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <msub> 
    <mi>
      R 
    </mi> 
    <mtext mathvariant="normal">
      in&nbsp; 
    </mtext> 
   </msub> 
   <annotation encoding="application/x-tex">
     R_{\text{in~}} 
   </annotation> 
  </semantics> 
 </math> and the voltage gain.</p><p>Input resistance:</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       R 
     </mi> 
     <mtext mathvariant="normal">
       in&nbsp; 
     </mtext> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <msub> 
      <mi>
        V 
      </mi> 
      <mtext mathvariant="normal">
        in&nbsp; 
      </mtext> 
     </msub> 
     <mrow> 
      <mi>
        Δ 
      </mi> 
      <msub> 
       <mi>
         I 
       </mi> 
       <mi>
         B 
       </mi> 
      </msub> 
     </mrow> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mrow> 
      <mo stretchy="true" form="prefix">
        ( 
      </mo> 
      <mn>
        10 
      </mn> 
      <mo>
        × 
      </mo> 
      <msup> 
       <mn>
         10 
       </mn> 
       <mrow> 
        <mo>
          − 
        </mo> 
        <mn>
          3 
        </mn> 
       </mrow> 
      </msup> 
      <mo stretchy="true" form="postfix">
        ) 
      </mo> 
     </mrow> 
     <mrow> 
      <mn>
        15 
      </mn> 
      <mo>
        × 
      </mo> 
      <msup> 
       <mn>
         10 
       </mn> 
       <mrow> 
        <mo>
          − 
        </mo> 
        <mn>
          6 
        </mn> 
       </mrow> 
      </msup> 
     </mrow> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mn>
      0.67 
    </mn> 
    <mi>
      k 
    </mi> 
    <mi>
      Ω 
    </mi> 
   </mrow> 
   <annotation encoding="application/x-tex">
     R_{\text{in~}} = \frac{V_{\text{in~}}}{\Delta I_{B}} = \frac{\left( 10 \times 10^{- 3} \right)}{15 \times 10^{- 6}} = 0.67k\Omega 
   </annotation> 
  </semantics> 
 </math> </p><p>Voltage gain:</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <mi>
      β 
    </mi> 
    <mo>
      × 
    </mo> 
    <mfrac> 
     <msub> 
      <mi>
        R 
      </mi> 
      <mi>
        L 
      </mi> 
     </msub> 
     <msub> 
      <mi>
        R 
      </mi> 
      <mrow> 
       <mi>
         i 
       </mi> 
       <mi>
         n 
       </mi> 
      </mrow> 
     </msub> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mrow> 
      <mi>
        Δ 
      </mi> 
      <msub> 
       <mi>
         I 
       </mi> 
       <mi>
         C 
       </mi> 
      </msub> 
     </mrow> 
     <mrow> 
      <mi>
        Δ 
      </mi> 
      <msub> 
       <mi>
         I 
       </mi> 
       <mi>
         B 
       </mi> 
      </msub> 
     </mrow> 
    </mfrac> 
    <mo>
      × 
    </mo> 
    <mfrac> 
     <msub> 
      <mi>
        R 
      </mi> 
      <mi>
        L 
      </mi> 
     </msub> 
     <msub> 
      <mi>
        R 
      </mi> 
      <mrow> 
       <mi>
         i 
       </mi> 
       <mi>
         n 
       </mi> 
      </mrow> 
     </msub> 
    </mfrac> 
   </mrow> 
   <annotation encoding="application/x-tex">
     \beta \times \frac{R_{L}}{R_{in}} = \frac{\Delta I_{C}}{\Delta I_{B}} \times \frac{R_{L}}{R_{in}} 
   </annotation> 
  </semantics> 
 </math> </p><p>Voltage gain</p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       A 
     </mi> 
     <mi>
       v 
     </mi> 
    </msub> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <msub> 
      <mi>
        V 
      </mi> 
      <mtext mathvariant="normal">
        out&nbsp; 
      </mtext> 
     </msub> 
     <msub> 
      <mi>
        V 
      </mi> 
      <mtext mathvariant="normal">
        in&nbsp; 
      </mtext> 
     </msub> 
    </mfrac> 
    <mo>
      = 
    </mo> 
    <mfrac> 
     <mrow> 
      <mn>
        3 
      </mn> 
      <mo>
        × 
      </mo> 
      <msup> 
       <mn>
         10 
       </mn> 
       <mrow> 
        <mo>
          − 
        </mo> 
        <mn>
          3 
        </mn> 
       </mrow> 
      </msup> 
     </mrow> 
     <mrow> 
      <mn>
        15 
      </mn> 
      <mo>
        × 
      </mo> 
      <msup> 
       <mn>
         10 
       </mn> 
       <mrow> 
        <mo>
          − 
        </mo> 
        <mn>
          6 
        </mn> 
       </mrow> 
      </msup> 
     </mrow> 
    </mfrac> 
    <mo>
      × 
    </mo> 
    <mfrac> 
     <mrow> 
      <mn>
        1 
      </mn> 
      <mo>
        × 
      </mo> 
      <msup> 
       <mn>
         10 
       </mn> 
       <mn>
         3 
       </mn> 
      </msup> 
     </mrow> 
     <mrow> 
      <mn>
        0.67 
      </mn> 
      <mo>
        × 
      </mo> 
      <msup> 
       <mn>
         10 
       </mn> 
       <mn>
         3 
       </mn> 
      </msup> 
     </mrow> 
    </mfrac> 
   </mrow> 
   <annotation encoding="application/x-tex">
     A_{v} = \frac{V_{\text{out~}}}{V_{\text{in~}}} = \frac{3 \times 10^{- 3}}{15 \times 10^{- 6}} \times \frac{1 \times 10^{3}}{0.67 \times 10^{3}} 
   </annotation> 
  </semantics> 
 </math> </p><p> 
 <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> 
   <mrow> 
    <msub> 
     <mi>
       A 
     </mi> 
     <mi>
       v 
     </mi> 
    </msub> 
    <mo>
      ≈ 
    </mo> 
    <mn>
      300 
    </mn> 
   </mrow> 
   <annotation encoding="application/x-tex">
     A_{v} \approx 300 
   </annotation> 
  </semantics> 
 </math> </p></div>