Question

A resistor R has its length doubled and diameter halved.find the new resistance.

Answer 1

Let the resistance be R.

Resistance of the wire is directly proportional to the length and inversely proportional to the Area of cross section.

Hence, the resistance will become doubled by doubling its length.

Now, by making the radius half, the area will decrease by the factor of four. Hence, the resistance will increase by the factor of four.

Hence, the new resistance will be = 2 × 4 × R = 8R

Hence, the new resistance will be 8 times the old value.