51 In Fig. 27-58, a voltmeter of resistance Rv -300 2 and an amme- ter of resist
ID: 2035365 • Letter: 5
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? RoExplanation / 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.