In a network, four capacitors C_{1} , C_{2} , C_{3} and C_{4} are connected as shown in the figure.

(a) Calculate the net capacitance in the circuit.

(b) If the charge on the capacitor C_{1} is 6\mu C,

(i) calculate the charge on the capacitors C_{3} and C_{4} , and

(ii) net energy stored in the capacitors C_{3} and C_{4} connected in series.

 

 
 

Answers (1)

The given capacitors are :

C_{1}=3\; \mu F____Connetced in parallel

C_{2}=6\; \mu F

C_{3}=4\; \mu F

C_{4}=12\; \mu F _____connected in series

(a) Let the capacitance across C_{2} and C_{1} is ;

        C_{12}=6+3=9\mu F

the capacitance across C_{3} and C_{4} is ;

C_{34}=\frac{12\times 4}{16}=3\mu F

Hence, the net capacitance would be ;

C_{net}=\frac{9\times 3}{12}=\frac{9}{4}\mu F

(b) The total charge flowing through the circuit

C_{net}V=\frac{9}{4}\times8=18\mu C

(ii) Since, Q=18\mu C

and         C_{34}=3\mu F

Then energy E_{34}=\frac{1}{2}\frac{Q^{2}}{C_{34}}

                    E_{34}=\frac{1}{2}\times \frac{(18\times 10^{-6})^{2}}{3\times 10^{-6}}

                    E_{34}=54\times 10^{-6}Joule

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