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Find the Equivalent Capacitance of the Network - CBSE (Science) Class 12 - Physics

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Question

Find the equivalent capacitance of the network shown in the figure, when each capacitor is of 1 μF. 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

The equivalent circuit is given below.

There are two capacitors in one branch in series. So, the equivalent capacitance of one branch will be

1/1+1/1=2muF

The arrangement will be further reduced to the form given below.

Now, both the capacitors are in parallel, so the equivalent capacitance will be

2+2=4μF

Therefore, the equivalent capacitance is 4 μF.

(i)

Voltage, V = 6 V

The charge in the network is given by

q=CV

Here, C is the equivalent capacitance.

Now,q=4×106×6  

=24×106 C=24 μC

(ii)

The energy stored in the network is given by
E=1/2CV2
  

=12×4×106×(6)2  

=12×4×36×106  

=72×106 J

=72 μJ

  Is there an error in this question or solution?

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Solution Find the Equivalent Capacitance of the Network Concept: Capacitors and Capacitance.
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