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Question

If at t=0, switch S is closed, at steady state find heat generated (H) in the given circuit having a battery of 16 volts.


A
640 μJ
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B
192 μJ
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C
1280 μJ
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D
320 μJ
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Solution

The correct option is A 640 μJ
Let us solve this problem using potential method, assigning potential to the known points, as shown in figure.


Using Kirchoff`s law at junction P,

(V016)×10+(V00)×4+(V00)×6=0

10V0160+4V0+6V0=0

20V0=160

V0=8 V

Using V0 we can get potential across C1, C2 and C3 as follows,

Potential difference across C1 is,

V1=(168)=80 V

Similarly V2 and V3 as,

V2=(80)=8 V

V3=(80)=8 V

Now using V1, V2 and V3 we can calculate energy stored in each capacitor as follows,

U1=12C1V12=12(10×106)(64)=320 μJ

U2=12C2V22=12(4×106)(64)=128 μJ

U3=12C3V32=12(6×106)(64)=192 μJ

Work done by battery:

WB=(Qthrough circuit)(VBattery)

Qthrough circuit=Qacross C1=(10×106)(8)=80 μC

WB=(80 μC)(16V)=1280 μJ

As we know that,
WB=Usystem + H

H=WBUsystem

H=WB(U1+U2+U3)

H=1280[320+128+192]

H=640 μJ

Hence, option (b) is the correct answer.

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