31. ​In a parallel plate capacitor, the distance between the plates is d and potential difference across the plates is V. Energy stored per unit volume between the plates of capacitor is

1. 1. Q²
      2V²

   
   
   

   2. ​

      1	ε0	V²
      2		d²

   
   
   

   3. ​

      1		V²
      2		ε0d²

   
   
   

   4. 1	ε0	V²
      2		d

   
   
   

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1. View Hint View Answer Discuss in Forum

   Energy stored per unit volume ​​
   

   =

   1

   ε0E² =

   1

   ε0

   V

   ²

   =

   1

   ε0

   V²

   ∵ E =

   V

   2

   2

   d

   2

   d²

   d

   Correct Option: B

   Energy stored per unit volume ​​
   

   =

   1

   ε0E² =

   1

   ε0

   V

   ²

   =

   1

   ε0

   V²

   ∵ E =

   V

   2

   2

   d

   2

   d²

   d

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32. A capacitor C₁ is charged to a potential difference V. The charging battery is then removed and the capacitor is connected to an uncharged capacitor C₂. The potential difference across the combination is

1. 1. VC1
      (C1 + C2)

   
   
   

   2. V		1 +	C2
      			C1

   
   
   

   3. V		1 +	C1
      			C2

   
   
   

   4. VC2
      (C1 + C2)

   
   
   

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1. View Hint View Answer Discuss in Forum

   Charge Q = C₁ V ​
   Total capacity of combination (parallel) ​C = C₁+ C₂​
   

   P.D. =	Q	=	C1V
   	C		C1 + C2

   Correct Option: A

   Charge Q = C₁ V ​
   Total capacity of combination (parallel) ​C = C₁+ C₂​
   

   P.D. =	Q	=	C1V
   	C		C1 + C2

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33. ​Three capacitors each of capacity 4µF are to be connected in such a way that the effective capacitance is 6 µF. This can be done by

1. 1. connecting two in parallel and one in series

   
   
   

   2. connecting all of them in series

   
   
   

   3. connecting them in parallel

   
   
   

   4. connecting two in series and one in parallel

   
   
   

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1. View Hint View Answer Discuss in Forum

   For series, C' =	C1 × C2	=	4 × 4	= 2μF
   	C1 + C2		4 + 4

   
   For parallel, C_eq = C' + C₃ = 2 - 4 = 6μF
   

   Correct Option: D

   For series, C' =	C1 × C2	=	4 × 4	= 2μF
   	C1 + C2		4 + 4

   
   For parallel, C_eq = C' + C₃ = 2 - 4 = 6μF
   

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34. A 4µF conductor is charged to  400 volts and then its plates are joined through a resistance of 1 kΩ. The heat produced in the resistance is

1. 1. 0.16 J ​

   
   
   

   2. ​1.28 J

   
   
   

   3. 0.64 J

   
   
   

   4. 0.32 J

   
   
   

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1. View Hint View Answer Discuss in Forum

   The energy stored in the capacitor =	1	CV²
   	2

   
   

   =	1	× 4 × 10-6 × (400)²
   	2

   
   ​= 0.325 ​
   This energy will be converted into heat in the resistor

   Correct Option: D

   The energy stored in the capacitor =	1	CV²
   	2

   
   

   =	1	× 4 × 10-6 × (400)²
   	2

   
   ​= 0.325 ​
   This energy will be converted into heat in the resistor

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35. A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates

1. 1. does not change

   
   
   

   2. becomes zero

   
   
   

   3. ​increases

   
   
   

   4. decreases

   
   
   

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1. View Hint View Answer Discuss in Forum

   If we increase the distance between the plates its capacity decreases resulting in higher potential as we know Q = CV. Since Q is constant (battery has been disconnected), on decreasing C, V will increase.

   Correct Option: C

   If we increase the distance between the plates its capacity decreases resulting in higher potential as we know Q = CV. Since Q is constant (battery has been disconnected), on decreasing C, V will increase.

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