26. What is the effective capacitance between points X and Y?
    

1. 1. ​24 µF ​

   
   
   

   2. 18 µF

   
   
   

   3. 12 µF

   
   
   

   4. 6 µF

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​ ​ ​
   Equivalent circuit
   ​
   ​

   Here,	C1	=	C2
   	C3		C4

   
   ​Hence, no charge will flow through 20µF
   ​ ​
   ​C₁ and C₂34 ​Hence, C' = 3 µF, C'' = 3 µF ​C' and C'' are in parallel. ​
   Hence net capacitance = C' + C'' = 3 + 3
   ​= 6 µF

   Correct Option: D

   ​ ​ ​
   Equivalent circuit
   ​
   ​

   Here,	C1	=	C2
   	C3		C4

   
   ​Hence, no charge will flow through 20µF
   ​ ​
   ​C₁ and C₂34 ​Hence, C' = 3 µF, C'' = 3 µF ​C' and C'' are in parallel. ​
   Hence net capacitance = C' + C'' = 3 + 3
   ​= 6 µF

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27. A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes .

1. 1. √2C

   
   
   

   2. 2C

   
   
   

   3. C/√2

   
   
   

   4. C/2

   
   
   

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1. View Hint View Answer Discuss in Forum

   When oil is placed between space of plates ​
   

   C =	2Aε0	..........(i)		∵ C =	KAε0	, if K = 2
   	d				d

   
   

   When oil is removed C' =	Aε0	......(ii)
   	d

   
   ​On comparing both equations, we get C ' = C/2

   Correct Option: D

   When oil is placed between space of plates ​
   

   C =	2Aε0	..........(i)		∵ C =	KAε0	, if K = 2
   	d				d

   
   

   When oil is removed C' =	Aε0	......(ii)
   	d

   
   ​On comparing both equations, we get C ' = C/2

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28. A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitor is

1. 1. U/2

   
   
   

   2. 3U/2

   
   
   

   3. U

   
   
   

   4. U/4

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​In Ist case when capacitor C connected with battery charged with the energy, ​
   U₁ = U (stored energy on capacitor). ​
   In IInd case, after disconnection of battery similar capacitor is connected in parallel with Ist capacitor then C_eq.=C' = 2C.
   

   Now,		=	1	q²		=
   	U1		2	C			C'
   	U2		1	q²			C
   			2	C'

   
   

   =	2C	(∵ C' = 2C)
   	C

   
   

   U2 =	U
   	2

   Correct Option: A

   ​In Ist case when capacitor C connected with battery charged with the energy, ​
   U₁ = U (stored energy on capacitor). ​
   In IInd case, after disconnection of battery similar capacitor is connected in parallel with Ist capacitor then C_eq.=C' = 2C.
   

   Now,		=	1	q²		=
   	U1		2	C			C'
   	U2		1	q²			C
   			2	C'

   
   

   =	2C	(∵ C' = 2C)
   	C

   
   

   U2 =	U
   	2

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29. Energy stored in a capacitor is​

1. 1. 1	QV
      2

   
   
   

   2. QV

   
   
   

   3. ​

      1
      QV

   
   
   

   4. ​

      2
      QV

   
   
   

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   Energy stored in capacitor ​
   

   =	1	CV² =	1	Q	y² (Q = CV)
   	2		2	V

   
   

   =	1	QV
   	2

   Correct Option: A

   Energy stored in capacitor ​
   

   =	1	CV² =	1	Q	y² (Q = CV)
   	2		2	V

   
   

   =	1	QV
   	2

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30. The capacity of a parallel plate condenser is 10 µF when the distance between its plates is 8 cm. If the distance between the plates is reduced to 4 cm then the capacity of this parallel plate condenser will be​​​

1. 1. 5 µF ​

   
   
   

   2. 10 µF

   
   
   

   3. 20 µF

   
   
   

   4. ​40 µF

   
   
   

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1. View Hint View Answer Discuss in Forum

   C = 10 µF​
   d = 8 cm ​
   C' = ?
   ​d' = 4 cm
   

   C =	A∊0	⇒ Cα	1
   	d		d

   
   ​If d is halved then C will be doubled. ​
   Hence, C' = 2C = 2 × 10 µF = 20 µF

   Correct Option: C

   C = 10 µF​
   d = 8 cm ​
   C' = ?
   ​d' = 4 cm
   

   C =	A∊0	⇒ Cα	1
   	d		d

   
   ​If d is halved then C will be doubled. ​
   Hence, C' = 2C = 2 × 10 µF = 20 µF

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