   Chapter 17, Problem 49P

Chapter
Section
Textbook Problem

Two wires A and B made of the same material and having the same lengths are connected across the same voltage source. If the power supplied to wire A is three times the power supplied to wire B, what is the ratio of their diameters?

To determine

The ratio of diameters of wires A and B made of same material.

Explanation

Given Info: The two wires A and B made of same material have length connected to same value of voltage. The power supplied to wire A is 3 times the power supplied to wire B.

Formula to calculate the resistance of wire A is,

RA=(ΔV)2PA (I)

• RA is the resistance of wire A,
• ΔV is the applied voltage,
• PA is the power delivered to wire A,

Formula to calculate the resistance of wire B is,

RB=(ΔV)2PB (II)

• RB is the resistance of wire B,
• PB is the power delivered to wire B,

Divide equation (I) by equation (II),

RARB=((ΔV)2PA)(PB(ΔV)2)

RARB=PBPA

Substitute PA=3PB in the above equation to find the ratio RARB,

RARB=PB3PB

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