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

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

View answer & explanation

Correct answer is C

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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