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
Correct Answer: Option C
Explanation
Resistance (alpha) (frac{length}{area})
(frac{R_Q}{R_P}) = (frac{L_QA_P}{L_PA_Q})
LQ = 2LP
DQ = 2DP
AP = (pi)(frac{(2D_P)^2}{2})
= (pi)DP
AQ = (pi)(frac{(D_P)^2}{2})
= (frac{1}{4})(pi)DP
therefore, (frac{R_Q}{R_P}) = (frac{2L_P times pi D_P}{L_P times frac{1}{4} pi D_P})
= 2 : 1