Question

A wire of resistance 100 ohm is doubled on itself.The percentage of decrease of its resistance is

(A)25% (B)50% (C)75% (D)20%

Answer 1

A wire of resistance 100 ohm is doubled on itself. The percentage of decrease of its resistance is

(A) 25% (B) 50% (C) 75% (D) 20%

Solution

Resistance of the wire

$$R = \rho \frac {l}{A},$$

where $l$ – the length of the wire, $A$ – the area of the wire, $\rho$ – resistivity of the wire.

When the wire is doubled on itself:

(1) The area of cross-section is doubled. If $A$ is the original C.S. area, now it is $2A$.

(2) The length becomes half i.e. $\frac{l}{2}$.

Resistance of the wire

$$R^{\prime} = \rho \frac {l / 2}{2 A} = \frac {1}{4} * \rho \frac {l}{A}.$$

But $\rho \frac{l}{A} = R = 100$ ohm.

$$R^{\prime} = \frac {1}{4} * 100 = 25 \text{ ohm}.$$

The percentage of decrease of its resistance is

$$\frac {R^{\prime}}{R} = \frac {25}{100} * 100\% = 25\%.$$

Answer: (A) 25%.