5. Consider the circuit shown. Elements A and B are wires made of steel, resisti

Question

5. Consider the circuit shown. Elements A and B are wires made of steel, resistivity 6.9?10-7 ?·m. Both have radius 0.10 mm (=1.0?10 -4 m.) Wire A is 0.40 m long, and wire B is 0.50 m long. Element R is a 5.0 ? resistor. The battery is an ideal 6.0 V battery. The unlabeled lines are wires that have negligible resistance.

a. Rank the resistances of A, B, and R in order of smallest to largest, identifying any that are equal.

b. Rank the currents through A, B, and R in order of smallest to largest, identifying any that are equal.

c. Rank the voltages across A, B, and R in order of smallest to largest, identifying any that are equal.

d. Rank the power dissipated in A, B, and R in order of smallest to largest, identifying any that are equal.

Explanation / Answer

Resistance of A = Ra = (rho)L/A = 6.9*10^-7 * 0.4/3.14*(0.1*10^-3)^2 = 8.7898 ohm
Resistance of B = Rb = (rho)L/A = 6.9*10^-7 * 0.5/3.14*(0.1*10^-3)^2 = 10.9872 ohm
R = 5 ohm

a) R < Ra < Rb
b) All the component are in series, so same current in every component
c) For same current, V is proportional to R
so Vr < Va < Vb
d) P = VI
for same current, P is proportional to V
Pr < Pa < Pb

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