Question 66

A 8Ω resistance wire is doubled on it. Calculate the new resistance of the wire.

Solution

When the wire is doubled the length will be halved and area will be double or twice

$$R = \frac{P\times L}{A}$$

$$R1 = \frac{P\times \frac{L}{2}}{2A}$$ , where R1 is the new resistance

$$\frac{R1}{R}=\frac{\frac{P\times \frac{L}{2}}{2A}}{\frac{P\times L}{A}}$$

$$\frac{R1}{R} = \frac{1}{4}$$

$$R1 = \frac{R}{4}$$

Putting the value of R=8 Ω,

$$R1=\frac{8}{4} = 2Ω$$

Option D is correct.

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