A wire P has half the diameter and half the length of a wire Q...

JAMB 1985

A wire P has half the diameter and half the length of a wire Q of similar material. The ratio of the resistance of P to that of Q is

A. 8 : 1
B. 4 : 1
C. 2 : 1
D. 1 : 1
E. 1 : 4

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Correct Answer: Option C

Explanation

Resistance \(\alpha\) \(\frac{length}{area}\)

\(\frac{R_Q}{R_P}\) = \(\frac{L_QA_P}{L_PA_Q}\)

L_Q = 2L_P

D_Q = 2D_P

A_P = \(\pi\)\(\frac{(2D_P)^2}{2}\)

= \(\pi\)D_P

A_Q = \(\pi\)\(\frac{(D_P)^2}{2}\)

= \(\frac{1}{4}\)\(\pi\)D_P

therefore, \(\frac{R_Q}{R_P}\) = \(\frac{2L_P \times \pi D_P}{L_P \times \frac{1}{4} \pi D_P}\)

= 2 : 1

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