The characteristics of five wires are given in the table. Length 2.0 m 2.0 m 2.0

Question

The characteristics of five wires are given in the table. Length 2.0 m 2.0 m 2.0 m 1.0 m 2.0 m Gauge #22 #22 #18 #18 #18 WireMaterial iron copper copper copper ron 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 9.7 × 10-8 ·m; and the value for copper is 1.72 x 10-8 ·m. 1. Of the five wires, which one has the smallest resistance? 2. Which one of the wires carries the smallest current when they are connected to iden tical batteries? 3. What is the resistance of wire B? (Show work.) 4. Wire B is connected to the terminals of a 1.5-V battery. W hat magnitude current flow through the wire?

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)

wire D has smallest resistance

2)

wire A

3)

resistance of wire B = 0.11 ohms

4)

current i = v/R = 1.5/0.11 = 13.6 A

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