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Capacitor question

2005 · Q170
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Capacitor question

2005 · Q170

NEETPhysicsCapacitorMCQ+4 / −1
A network of four capacitors of capacity equal to C1 = C, C2 = 2C, C3 = 3C and C4 = 4C are connected to a battery as shown in the figure. The ratio of the charges on C2 and C4 is

AIPMT 2005 Physics - Capacitor Question 22 English
  1. A
    4/7
  2. B
    3/22
  3. C
    7/4
  4. D
    22/3
View written solutionFree

Correct answer: B

AIPMT 2005 Physics - Capacitor Question 22 English Explanation

Equivalent capacitance for three capacitors (C1, C2 & C3) in series is given by

1Ceq.=1C1+1C2+1C3{1 \over {{C_{eq.}}}} = {1 \over {{C_1}}} + {1 \over {{C_2}}} + {1 \over {{C_3}}}Ceq.​1​=C1​1​+C2​1​+C3​1​

=C2C3+C3C1+C1C2C1C2C3 = {{{C_2}{C_3} + {C_3}{C_1} + {C_1}{C_2}} \over {{C_1}{C_2}{C_3}}}=C1​C2​C3​C2​C3​+C3​C1​+C1​C2​​

⇒Ceq.=C1C2C3C2C3+C3C1+C1C2 \Rightarrow {C_{eq.}} = {{{C_1}{C_2}{C_3}} \over {{C_2}{C_3} + {C_3}{C_1} + {C_1}{C_2}}}⇒Ceq.​=C2​C3​+C3​C1​+C1​C2​C1​C2​C3​​

⇒Ceq.=2(2C)(3C)C(2C)+(2C)(3C)+(3C)C=611C \Rightarrow {C_{eq.}} = {{2\left( {2C} \right)\left( {3C} \right)} \over {C\left( {2C} \right) + \left( {2C} \right)\left( {3C} \right) + \left( {3C} \right)C}} = {6 \over {11}}C⇒Ceq.​=C(2C)+(2C)(3C)+(3C)C2(2C)(3C)​=116​C

⇒\Rightarrow⇒ Charge on capacitors (C1, C2 & C3) in series

=CeqV=6C11V = {C_{eq}}V = {{6C} \over {11}}V=Ceq​V=116C​V

Charge on capacitor C4=C4V=4CV{C_4} = {C_4}V = 4CVC4​=C4​V=4CV

Charge on C2Charge on C4=6C11V4CV=611×14=322{{Charg e\,on\,{C_2}} \over {Charg e\,on\,{C_4}}} = {{{{6C} \over {11}}V} \over {4CV}} = {6 \over {11}} \times {1 \over 4} = {3 \over {22}}ChargeonC4​ChargeonC2​​=4CV116C​V​=116​×41​=223​

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