The figure shows a portion of a circuit. Resistor are known and indicated on diagram and voltmeters are identical. If voltmeters v1 and v2 reads 7.5V and 5V respectively then reading of v3.

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0 V

10 V

2.5 V

3.0 V

answer is D.

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Detailed Solution

[Concept]: Since all voltmeters are identical there resistors have resistance Rv V1=i1Rv V2=i2Rv V3=i3Rv [Step 1]: i1Rvi2Rv=V1V2⇒i1i2=7.55=32⇒i1=32 i2 ⇒let i2=x and i1=32x Step 2]: loop1 containing V1 and V2: 9i1-14i2+V2-V1=09×32x−14x+5−7.5=013.5x-14x=2.5[ Step 3 ]:x=−5.0A=I2[ Step 4 ]:i1=32 i2 =32(-5)⇒−7.5A=I1V1=i1Rv⇒7.5=7.5Rv Hence resistance of voltmeter(Rv)is 1Ω[ Step 6 ]: Step 2]: loop2 containing V1 and V3: 24I3=−7.5−7.5×9=24I3=−75 Step 7]: I3=−3A Hence V3=i3Rv=3(1)=3.0V

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