Question

Two metallic wire A and B are connecting in series wire A has length l and radius r while wire B has length 2l and radius 2r. Find the ratio of the total resistances of series combination and the resistances of wire A if both the wire are of same.

Answer 1

Suppose the resistivity of both the wires is ‘q’.

Resistance of wire A is, R_a = ql/(πr²)

Resistance of wire B is, R_b = q(2l)/[π(2r)²] = ql/(2πr²)

Now, the resistance when they are connected in series is, R = R_a + R_b = (3/2)[ql/(πr²)]

So, the required ratio is, R : R_a = (3/2)[ql/(πr²)] : ql/(πr²)

=> R : R_a = 3 : 2