Name SinthM ID Quiz 5 (30%) A resistive metal wire has a diameter D and length L

Question

Name SinthM ID Quiz 5 (30%) A resistive metal wire has a diameter D and length L. When a potential difference applied to both ends of the wire, it generates heat at a rate of P. Now cut the wire into two halves and pull one half into a new wire of a diameter ! D. Conmect this new wire back to the other half and apply the same potential difference AV. What is the rate of heat generated by the wire now? Ignore the resistivity change due to temperature of the wire. 2. (30%) Find the potential difference across R), when R.-30, R,-90, and R,-60 3. (40%) The voltage source sends out a step pulse from OV to at r = o. Sketch out the voltage over the resister R as a funaction of time f, and find the value of t when the voltage over this resis er reads 50% of

Explanation / Answer

We know that

R = rho L/A

R1 = rho L/(pi d^2/4) = 4 rho L/(pi D^2)

Power dissipated will be:

P1 = V^2/R1

P1 = V^2 pi D^2/4 rho L

After the wire is cut, the new resistance will be:

R2 = rho L/(pi D^2/16)

P2 = V^2/R2 = V^2/(16 rho L/pi D^2)

Since the voltage remains the same

P2 = V^2 pi D^2/16 rho L

P1/P2 = 16/4 = 4

P2 = P1/4

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