GP Electricity

Two conducting wires A and B are made of same material. If the length of B is twice that of A and the radius of circular cross-section of A is twice that of B, then their resistances RA and RB are in the ratio

  1. 1 : 2
  2. 2 : 1
  3. 1 : 4
  4. 1 : 8

Answer

Resistance of wire is directly proportional to the length and inversely proportional to the cross-sectional area (square of radius).

LB = 2 LA

rA = 2 rB which means r2A = 4 r2B

RA = LA/r2A = 1/8 RB

The correct option is D.