Question 663: Electrostatics & Capacitance

Question

A network of four capacitors of capacity equal to C
1
= C, C
2
= 2C, C
3
= 3C and C
4
= 4C are connected to a battery as shown in the figure. The ratio of the charges on C
2
and C
4
is

Accepted Answer

Equivalent capacitance for three capacitors (C
1
, C
2
& C
3
) in series is given by
$${1 \over {{C_{eq.}}}} = {1 \over {{C_1}}} + {1 \over {{C_2}}} + {1 \over {{C_3}}}$$
$$ = {{{C_2}{C_3} + {C_3}{C_1} + {C_1}{C_2}} \over {{C_1}{C_2}{C_3}}}$$
$$ \Rightarrow {C_{eq.}} = {{{C_1}{C_2}{C_3}} \over {{C_2}{C_3} + {C_3}{C_1} + {C_1}{C_2}}}$$
$$ \Rightarrow {C_{eq.}} = {{2\left( {2C} ight)\left( {3C} ight)} \over {C\left( {2C} ight) + \left( {2C} ight)\left( {3C} ight) + \left( {3C} ight)C}} = {6 \over {11}}C$$
$$ \Rightarrow $$ Charge on capacitors (C
1
, C
2
& C
3
) in series
$$ = {C_{eq}}V = {{6C} \over {11}}V$$
Charge on capacitor $${C_4} = {C_4}V = 4CV$$
$${{Charg e\,on\,{C_2}} \over {Charg e\,on\,{C_4}}} = {{{{6C} \over {11}}V} \over {4CV}} = {6 \over {11}} 	imes {1 \over 4} = {3 \over {22}}$$

Answer

4/7

Answer

3/22

Answer

7/4

Answer

22/3

Electrostatics & Capacitance

A network of four capacitors of capacity equal to C 1 = C, C 2 = 2C, C 3 = 3C and C 4 = 4C are connected to a battery as shown in the figure. The ratio of the charges on C 2 and C 4 is

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