Seven capacitors,each of capacitance 2 mu F,a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the capacitance of each capacitor be $C = 2 \mu F$. We need an equivalent capacitance $C_{eq} = \frac{6}{13} \mu F$.If we connect $n$ capacito

Vedclass · Accepted Answer

$3$ capacitors in parallel and then $4$ capacitors in series.

Vedclass · Answer

(C) Let the capacitance of each capacitor be $C = 2 \mu F$. We need an equivalent capacitance $C_{eq} = \frac{6}{13} \mu F$.If we connect $n$ capacitors in parallel,their equivalent capacitance is $nC$. If we connect $m$ such parallel groups in series,the total equivalent capacitance $C_{eq}$ is given by $\frac{1}{C_{eq}} = \frac{1}{nC} + \frac{1}{nC} + \dots + \frac{1}{nC} = \frac{m}{nC}$.Given $C = 2 \mu F$,we have $C_{eq} = \frac{nC}{m} = \frac{n 	imes 2}{m} = \frac{6}{13}$.This implies $\frac{n}{m} = \frac{3}{13}$,which does not use all $7$ capacitors. Alternatively,consider a configuration where $3$ capacitors are in parallel $(C_p = 3C = 6 \mu F)$ and this group is in series with $4$ individual capacitors ($C = 2 \mu F$ each).The equivalent capacitance is $\frac{1}{C_{eq}} = \frac{1}{3C} + \frac{1}{C} + \frac{1}{C} + \frac{1}{C} + \frac{1}{C} = \frac{1}{3C} + \frac{4}{C} = \frac{1 + 12}{3C} = \frac{13}{3C}$.Thus,$C_{eq} = \frac{3C}{13} = \frac{3 	imes 2}{13} = \frac{6}{13} \mu F$.Therefore,the correct configuration is $3$ capacitors in parallel and $4$ capacitors in series.

Seven capacitors,each of capacitance $2 \mu F$,are connected in a configuration to obtain an effective capacitance of $\frac{6}{13} \mu F$. The combination that will achieve this is:

Similar Questions

The network of six capacitors is as shown in the figure. The equivalent capacitance between $A$ and $B$ is

Find the equivalent capacitance of the circuit between points $A$ and $B$.

Two capacitors of same capacity are first joined in series and then in parallel. The ratio of resultant capacity in series to that in parallel combination will be

Three capacitors each of capacitance $C$ and of breakdown voltage $V$ are joined in series. The capacitance and breakdown voltage of the combination will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module