Question 30: Electrostatics & Capacitance

Question

Three capacitors C
1
, C
2
and C
3
are connected as shown in the figure below. If capacitor C
3
breaks down electrically, the change in total charge on the combination of capacitors is
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1ls1lk3o8/1a768c2d-2e02-4b02-bfbe-45f3a1793431/c3f2ca70-c01c-11ee-a44e-4fd06148d0b3/file-6y3zli1ls1lk3o9.png?format=png)

Accepted Answer

Since capacitors C1 and C2
are parallel, so their equivalent capacitance will be (C1 + C2). $\$ 
Now, (C1 + C2) and C3 are in series, so the net equivalent capacitance of circuit will be, $\$
${1 \over C} = {1 \over {{C_3}}} + {1 \over {{C_1} + {C_2}}} = {{{C_1} + {C_2} + {C_3}} \over {({C_1} + {C_2}){C_3}}}$ $\$
or, $C = {{({C_1} + {C_2}){C_3}} \over {{C_1} + {C_2} + {C_3}}}$ $\$
Since V is the voltage of the battery, so charge on this system,$\$
$q = CV \Rightarrow q = {{({C_1} + {C_2}){C_3}V} \over {({C_1} + {C_2} + {C_3})}}$ $\$
If the capacitance C3 breaks down, then total equivalent capacitance will become
$C' = {C_1} + {C_2}$ $\$
$	herefore$ New charge stored,
$q' = C'V$
$ \Rightarrow q' = ({C_1} + {C_2})V$ $\$
Now, change in total charge,
$\Delta q = q' - q$ [$\because$ $q' > q$]
$ = ({C_1} + {C_2})V - {{({C_1} + {C_2}){C_3}V} \over {{C_1} + {C_2} + {C_2}}}$ $\$
or, $\Delta q = ({C_1} + {C_2})V\left[ {1 - \left( {{{{C_3}} \over {{C_1} + {C_2} + {C_3}}}} ight)} ight]$

Answer

$({C_1} + {C_2})V\left[ {1 - \left( {{{{C_3}} \over {{C_1} + {C_2} + {C_3}}}} \right)} \right]$

Answer

$({C_3} + {C_2})V\left[ {1 - \left( {{{{C_1}} \over {{C_1} + {C_2} + {C_3}}}} \right)} \right]$

Answer

$({C_1} + {C_2})V\left[ {1 - \left( {{{{C_2} + {C_1}} \over {{C_1} + {C_3}}}} \right)} \right]$

Answer

$({C_1} + {C_2})V\left[ {1 - \left( {{{{C_2}} \over {{C_1} + {C_3}}}} \right)} \right]$

Electrostatics & Capacitance

Three capacitors C 1 , C 2 and C 3 are connected as shown in the figure below. If capacitor C 3 breaks down electrically, the change in total charge on the combination of capacitors is

Choose the correct answer: