2. The characteristics of five wires are given in the table. Gauge #22 #22 #18 #

Question

2. The characteristics of five wires are given in the table. Gauge #22 #22 #18 #18 #18 Wire Length Material ron copper copper 2.0 m 2.0 m 2.0 m 1.0 m 2.0 m D copper iron The gauge is a measure of the diameter of the wire; and #18 corresponds to a diameter of 1 .2 × 10-3 m; and #22 corresponds to a diameter of 6.4 10-4 m. The resistivity of iron is 9.7x 10-8 ? -m; and the value for copper is 1.72x 10-8 ?-m a. What is the resistance of wire D? b. Which wire has the lowest resistance? Justify your answer c. If a current of 3 A flows in the wire, how much energy is dissipated in two minutes?

Explanation / Answer

resistance R = rho*L/(pi*d^2/4) = 4*rho*l/(pi*d^2)

d = diameter

RA = (4*9.7*10^-8*2)/(pi*(6.4*10^-4)^2) = 0.6 ohm

RB = (4*1.72*10^-8*2)/(pi*(6.4*10^-4)^2) = 0.11 ohm

RC = (4*1.72*10^-8*2)/(pi*(1.2*10^-3)^2) = 0.03 ohm

RD = (4*1.72*10^-8*1)/(pi*(1.2*10^-3)^2) = 0.015 ohm

RE = (4*9.7*10^-8*2)/(pi*(1.2*10^-3)^2) = 0.172 ohm

1)

0.015 ohm

2)

wire D has smallest resistance

3)

energy dissipated E = I^2*RD*t

E = 3^2*0.015*120 = 16.2 J

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