Two conducting wires A and B are made of same material

• 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 R_A and R_B 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).

L_B = 2 L_A

r_A = 2 rB which means r²_A = 4 r²_B

R_A = L_A/r²_A = 1/8 R_B

The correct option is D.