51 In Fig. 27-58, a voltmeter of resistance Rv -300 2 and an amme- ter of resist

Question

51 In Fig. 27-58, a voltmeter of resistance Rv -300 2 and an amme- ter of resistance RA3.00 2 are be- Fig. 27-57 Problem 50 ing used to measure a resistance R in a circuit that also contains a resis- tance Ro-100 2 and an ideal bat tery of emf 8- 12.0 V. Resistance R is given by R-Vli, where V is the potential across R and i is the amme- ter reading. The voltmeter reading is v', which is V plus the potential dif- ference across the ammeter. Thus, the ratio of the two meter readings is not R but only an apparent resistance Fig. 27-58 Problem 51 R, V,/i. If R-85.0 ?, what are (a) the ammeter reading, (b) the voltmeter reading, and (c) R'? (d) If RA is decreased, does the difference between R, and R increase, decrease, or remain the same? Ro

Explanation / Answer

a) Equivalent resistance,

Req = Ro + Rv*(R + RA)/(Rv + R + RA)

= 100 + 300*(85 + 3)/(300 + 85 + 3)

= 168 ohms

current through Ro, Io = E/Req

= 12/168

= 0.0714 A

ammeter reading, i = Io*Rv/(Rv + R + RA)

= 0.0714*300/(300 + 85 + 3)

= 0.0552 A <<<<<<<<----------------Answer

b) Volt meter reading, V' = i*(R + RA)

= 0.0552*(85 + 3)

= 4.86 V <<<<<<<<----------------Answer

c) R' = V'/i

= 4.86/0.0552

= 88.0 ohms <<<<<<<<----------------Answer

d) decreases.

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