Single Choice

The resistance of a wire is $$R$$. It is bent at the middle by $$180^{\circ}$$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

A$$2R$$
B$$R/2$$
C$$R/4$$
Correct Answer
D$$R/8$$

Solution

Resistance of wire $$(R) = \rho \dfrac {1}{4}$$
If wire is bent in the middle then
$$l' = \dfrac {1}{2}, A' = 2A$$
$$\therefore$$ New resistance, $$R' = \rho \dfrac {l'}{A'} = \dfrac {\rho \dfrac {1}{2}}{2A} = \dfrac {\rho l}{4A} = \dfrac {R}{4}$$.

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