In the figure a voltmeter of resistance RV = 426 ? and an ammeter of resistance

Question

In the figure a voltmeter of resistance RV = 426 ? and an ammeter of resistance RA = 4.28 ? are being used to measure a resistance R in a circuit that also contains R0 = 100 ? and an ideal battery of emf ? = 12.0 V. Resistance R is given by V/i, where V is the potential across R and i is the ammeter reading. The voltmeter reading is V', which is V plus the potential difference across the ammeter. Thus, the ratio of the two meter readings is not R but only anapparent resistance R' = V'/i. If R = 104 ?, what are (a) the ammeter reading in milliamperes, (b) the voltmeter reading, and (c) R'?

Explanation / Answer

a)Req=(104+4.28)||426+100=108.28*426/(108.28+426)+100=186.3ohm

I=E/Req*426/(104+4.28+426)=12/186.3*426/(104+4.28+426)=0.0514A

b)V=(104+4.28)*0.0514=5.57V
c)R'=V'/I=5.57/0.0514=108.4ohm

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