The charge on the 4 mu F capacitor in the giv | vedclass

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(A) The circuit consists of a $10 	ext{ V}$ battery connected in parallel with a $3 \mu F$ capacitor and a branch containing a $4 \mu F$ capacitor in

Vedclass · Accepted Answer

$24$

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(A) The circuit consists of a $10 	ext{ V}$ battery connected in parallel with a $3 \mu F$ capacitor and a branch containing a $4 \mu F$ capacitor in series with a parallel combination of $1 \mu F$ and $5 \mu F$ capacitors.First,calculate the equivalent capacitance of the parallel combination of $1 \mu F$ and $5 \mu F$ capacitors:$C_p = 1 \mu F + 5 \mu F = 6 \mu F$Now,the upper branch consists of a $4 \mu F$ capacitor in series with this $6 \mu F$ equivalent capacitor. The equivalent capacitance of this upper branch $(C_{eq})$ is:$\frac{1}{C_{eq}} = \frac{1}{4 \mu F} + \frac{1}{6 \mu F} = \frac{3+2}{12 \mu F} = \frac{5}{12 \mu F}$$C_{eq} = \frac{12}{5} \mu F = 2.4 \mu F$The potential difference across this entire upper branch is equal to the battery voltage,$V = 10 	ext{ V}$.The charge $Q$ on the equivalent capacitor of the upper branch is:$Q = C_{eq} 	imes V = 2.4 \mu F 	imes 10 	ext{ V} = 24 \mu C$Since the $4 \mu F$ capacitor and the $6 \mu F$ equivalent capacitor are in series,the charge on each is the same and equal to the total charge of the branch.Therefore,the charge on the $4 \mu F$ capacitor is $24 \mu C$. The correct option is $(a)$.

The charge on the $4 \mu F$ capacitor in the given circuit is (in $\mu C$)

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