36. Two condensers, one of capacity C and other of capacity C/2 are connected to a V-volt battery, as shown.​​​[2007] ​The work done in charging fully both the condensers is​​​
    

1. 1. 1	CV²
      4

   
   
   

   2. 3	CV²
      4

   
   
   

   3. 1	CV²
      2

   
   
   

   4. 2CV².

   
   
   

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   ​Work done = Change in energy ​
   

   =	1		C +	C		V² =	1		3C		V² =	3CV²
   	2			2			2		2			4

   Correct Option: B

   ​Work done = Change in energy ​
   

   =	1		C +	C		V² =	1		3C		V² =	3CV²
   	2			2			2		2			4

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37. Two parallel metal plates having charges + Q and –Q face  each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will

1. 1. remain same

   
   
   

   2. ​become zero

   
   
   

   3. ​increases

   
   
   

   4. decrease

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​Electric field ​ ​
   

   E =	σ	=	Q
   	ε		Aε

   
   ε of kerosine oil is more than that of air. ​
   As ε increases, E decreases.

   Correct Option: D

   ​Electric field ​ ​
   

   E =	σ	=	Q
   	ε		Aε

   
   ε of kerosine oil is more than that of air. ​
   As ε increases, E decreases.

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38. A series combination of n₁ capacitors, each of value C₁, is charged by a source of potential difference 4 V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C₂ , in terms of C₁, is then​​​

1. 1. 2C1

      n1n2

      ​

   
   
   

   2. ​

      16	n2	C1
      	n1

   
   
   

   3. 2	n2	C1
      	n1

   
   
   

   4. 16C1

      n1n2

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​In series, Ceff =	C1
   	n1

   
   

   ∴ Energy stored, Es =	1	Ceff C2² =	1	C1	16V²
   	2		2	n1

   
   

   = 8V²	C1
   	n1

   
   ​In parallel, C_eff = n₂ C₂ ​ ​
   

   Energy stored, Ep =	2	n2C2V²
   	2

   
   

   ∴	8V²C1	=	1	= n2C2V²
   	n1		2

   
   

   ⇒ C2 =	16C1
   	n1n2

   Correct Option: D

   ​In series, Ceff =	C1
   	n1

   
   

   ∴ Energy stored, Es =	1	Ceff C2² =	1	C1	16V²
   	2		2	n1

   
   

   = 8V²	C1
   	n1

   
   ​In parallel, C_eff = n₂ C₂ ​ ​
   

   Energy stored, Ep =	2	n2C2V²
   	2

   
   

   ∴	8V²C1	=	1	= n2C2V²
   	n1		2

   
   

   ⇒ C2 =	16C1
   	n1n2

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39. A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is :

1. 1. 1	ε0E²
      2

   
   
   

   2. E²Ad/ε₀ ​

   
   
   

   3. 1	ε0E²Ad
      2

   
   
   

   4. ε₀EAd

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​The energy stored by a capacitor ​​​​​...(i) ​
   

   U =	1	CV²...........(i)
   	2

   
   V is the p.d. between two plates of the capacitor. ​The capacitance of the parallel plate capacitor ​​V = E.d. ​ ​
   

   C =	Aε0
   	d

   
   Substituting the value of C in equation (i) ​
   

   U =	1	Aε0	(Ed)² =	1	Aε0E²d
   	2	d		2

   Correct Option: C

   ​The energy stored by a capacitor ​​​​​...(i) ​
   

   U =	1	CV²...........(i)
   	2

   
   V is the p.d. between two plates of the capacitor. ​The capacitance of the parallel plate capacitor ​​V = E.d. ​ ​
   

   C =	Aε0
   	d

   
   Substituting the value of C in equation (i) ​
   

   U =	1	Aε0	(Ed)² =	1	Aε0E²d
   	2	d		2

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40. Two thin dielectric slabs of dielectric constants K₁ and K₂ (K₁ ≤ K₂) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field ‘E’ between the plates with distance ‘d’ as measured from plate P is correctly shown by :
    

1. 1. 

   
   
   

   2. 

   
   
   

   3. ​

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   Electric field, E ∝ 1/K ​
   As K₁ < K₂ so E₁ > E₂ ​
   Hence graph (c) correctly dipicts the variation of electric field E with distance d.

   Correct Option: C

   Electric field, E ∝ 1/K ​
   As K₁ < K₂ so E₁ > E₂ ​
   Hence graph (c) correctly dipicts the variation of electric field E with distance d.

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