Question

(a) State four factors on which the resistance of a conductor depends.
​(b) A piece of wire of resistance 20 Ω is drawn out so that its length is increased to twice its original length. Calculate the resistance of the wire in the new situation.

Answer 1

(a) The resistance of a conductor depends on the following factors:

(i) Shape of the conductor
(ii) Size of the conductor
(iii) Material of the conductor
(iv) Temperature of the conductor

(b) Initial resistance = 20 Ω

When the length of the resistance is increased, it's volume remains constant.

According to relation,

$$\begin{gathered} R\propto \frac{l}{A}\propto \frac{l^2}{V} \\ \because V=\mathrm{Constant} \\ \therefore R\mathit{}\mathit{\propto }\mathit{}{l}^{\mathit{2}} \end{gathered}$$

$$\begin{gathered} \Rightarrow \frac{R_{\mathrm{i}}}{R_{\mathrm{f}}}=\frac{l_{\mathrm{i}}^2}{l_{\mathrm{f}}^2} \\ \Rightarrow \frac{20\mathrm{\Omega }}{R_{\mathrm{f}}}=\frac{l_{\mathrm{i}}^2}{(2l_{\mathrm{i}}{)}^2}=\frac{1}{4} \\ \Rightarrow R_{\mathrm{f}}=80\mathrm{\Omega } \end{gathered}$$