Three wires of the same diameter are connected in turn between two points mainta

ID: 2145444 • Letter: T

Question

Three wires of the same diameter are connected in turn between two points maintained at

a constant potential difference. Their resistivities and lengths are r and L (wire A), 1.2r

and 1.2L (wire B), and 0.9r and L (wire C).

a. How does the rate at which energy is transferred to thermal energy vary with the

resistance of the wire? In other words, does the dU/dt increase with increasing

resistance or does it decrease with increasing resistance? Remember, the potential

across each wire is the same. Explain.

b. Using your answer from part (a), rank the wires according to the rate at which

energy is transferred to thermal energy within them, greatest to least.

since R=ro*l/A

also diameter is same hence R only depends on ro*l.

for wire 1(R1)=rL

for wire 2(R2)=1.44rL

for wire 3(R3)=0.9rL

a)potential is same i.e. V constant

V=IR

I=V/R

for wire 1(I1)=V/R1=V/rL

for wire 2(I2)=V/R2=V/1.44rL

for wire 3(I3)=V/R3=V/0.9rL

now energy=I^2Rt

energy for wire 1=(V^2/rL)t

energy for wire 2=(V^2/1.44rL)t

energy for wire 3=(V^2/0.9rL)t

hence dU/dt decreases as increase in resistance.

b)energy tranferring rate

wire3>wire1>wire2

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