Question

In the circuit shown in the figure when switch S1 is closed and S2 is open, the ideal voltmeter shows a reading 18V. When switch S2 is closed and S1 is open, the reading of the voltmeter is 24V. When S1 and S2 both are closed the voltmeter reading will be

A
14.4V
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B
20.6V
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C
24.2V
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D
10.8V
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Solution

The correct option is A 14.4VTheinternalresistanceofthecellandEisthee.m.fofthesourceso,V×(r+R)=RENowinfirstcaseR=6ΩandV=18VsecondcaseR=12ΩandV=24VSo,18×(r+6)=6×E..........(1)And24×(r+12)=12×E........(2)⇒2(r+12)=3×(r+6)or,r=6ΩNowwegetE=36Vsowhenbothswitchesclosedthenequivalentresistancewillbe6×12(6+12)=4ΩHencethevoltmeterreadingwillbegotfromER=V(r+R)⇒36×4=V(6+4)Hence,V=14.4V

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