The figure below shows a resistor of resistance R = 8.00 resistor connected to a
ID: 2238722 • Letter: T
Question
The figure below shows a resistor of resistance R = 8.00 resistor connected to an ideal 12.0 V battery by means of two copper wires. Each wire has length 20.0 cm and radius 1.00 mm. In dealing with such circuits, we generally neglect the potential differences along wires and the transfer of energy to thermal energy in them. Check the validity of this neglect for the circuit by answering the following questions.
(a) What is the potential difference across the resistor? (Enter your answer to 6 significant figures for comparison.)
V
(b) What is it across each of the two sections of wire?
mV
(c) At what rate is energy lost to thermal energy in the resistor?
W
(d) At what rate is it lost in each of the two sections of wire?
W
Explanation / Answer
resistance of wire = rho*l/A = 1.7E-8 *20E-2/pi E-6 = 0.001082 ohm
therefore Req o circuit = 8 +0.002164 = 8.002164 ohm
a) Vr = V*R/Req = 12*8/8.002164 = 11.996754 V
b)Vwire = V*Rwire/Req = 0.001622 V
c) Pr = Vr^2/R = 17.990263 W
d)Pwires = Vwire^2/Rwire = 0.002432 W
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