Five capacitors of capacitances $C_1 = C_2 = C_3 = C_4 = 10\ \mu F$ and $C_5 = 2.5\ \mu F$ are connected as shown, along with a battery of 50 V. The equivalent capacitance and the charges on each capacitor respectively are:

A 5 $\mu F$, 125 $\mu C$ on all capacitors

B 5 $\mu F$, 250 $\mu C$ on all capacitors

C 4 $\mu F$, 250 $\mu C$ on $C_1$ to $C_4$ and 125 $\mu C$ on $C_5$

D 5 $\mu F$, 125 $\mu C$ on $C_1$ to $C_4$ and 25 $\mu C$ on $C_5$

The answer is A.

Solution

$C_1 = C_2 = C_3 = C_4 = 10\ \mu F$, $C_5 = 2.5\ \mu F$
$C_1$, $C_2$, $C_3$, $C_4$ are in series: $\frac{1}{C'} = 4 \times \frac{1}{10} \Rightarrow C' = 2.5\ \mu F$
$C'$ is in parallel with $C_5$ across the 50 V battery.
$C_{eq} = C' + C_5 = 2.5 + 2.5 = 5\ \mu F$
$q_{C_1} = q_{C_2} = q_{C_3} = q_{C_4} = 50 \times 2.5 = 125\ \mu C$
$q_{C_5} = 50 \times 2.5 = 125\ \mu C$ So $C_{eq}$ = 5 $\mu F$ and the charge is 125 $\mu C$ on all capacitors.

Electrostatic Potential and Capacitance in past papers

76 questions from this chapter have appeared across 27 exam years.

Five capacitors of capacitances $C_1 = C_2 = C_3 = C_4 = 10\ \mu F$ and $C_5 = 2.5\ \mu F$ are connected as shown, along with a battery of 50 V. The equivalent capacitance and the charges on each capacitor respectively are:

Solution

Electrostatic Potential and Capacitance in past papers

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