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Electrostatic Potential And Capacitance

Question
CBSEENPH12039174

Find the equivalent capacitance of the network shown in the figure, when each capacitor is of 1 straight mu F. When the ends X and Y are connected to a 6 V battery, find out

(i) the charge and

(ii) the energy stored in the network

Solution

Equivalent circuit can be drawn as, 

In the above circuit, in one branch there are two capacitors in series. 

Therefore, resultant capacitance is, 
1 over 1 plus 1 over 1 equals 2 space mu F

The circuit can be further re-arranged as, 

We can see the two capacitors are in parallel.

Therefore, their resultant capacitance is, 
Cres = 2 + 2 = 4 straight mu space straight F

Voltage of the battery = 6V

i) Charge across the capacitor, q = CV = 4 straight space cross times straight space 10 to the power of negative 6 end exponent straight space cross times straight space 6 straight space equals straight space 24 cross times straight space 10 to the power of negative 6 end exponent straight space equals straight space 24 straight space μC
ii) Energy stored in the capacitor, E is given by, 
              1 half C V squared space equals space 1 half cross times 4 space cross times space 10 to the power of negative 6 end exponent space cross times space left parenthesis 6 right parenthesis squared space

italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space equals space 72 space cross times space 10 to the power of negative 6 end exponent space J space equals space 72 space mu J

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