Q166 / 170 · Manipal (MET) 2018 · Physics
A wire of length 100 cm is connected to a cell of emf 2 V and negligible internal resistance. The resistance of the wire is $3 \Omega$, the additional resistance required to produce a potential difference of $1 \mathrm{mV} / \mathrm{cm}$ is
- A$60 \Omega$
- B$47 \Omega$
- Correct answerC$57 \Omega$
- D$35 \Omega$
Solution
Resistance per unit length of wire
$x=\frac{3}{100}=3 \times 10^{-2} \Omega \mathrm{~cm}^{-1}$
Equivalent length of wire $l^{\prime}=\frac{R+3}{3 \times 10^{-2}}$ $R$ being additional resistance $\begin{array}{rlrl} & & \frac{E}{k} & =\frac{R+3}{3 \times 10^{-2}} \\ \Rightarrow \quad & \frac{2}{1 \times 10^{-3}} & =\frac{R+3}{3 \times 10^{-2}} \\ \Rightarrow \quad & R & =57 \Omega \end{array}$
Equivalent length of wire $l^{\prime}=\frac{R+3}{3 \times 10^{-2}}$ $R$ being additional resistance $\begin{array}{rlrl} & & \frac{E}{k} & =\frac{R+3}{3 \times 10^{-2}} \\ \Rightarrow \quad & \frac{2}{1 \times 10^{-3}} & =\frac{R+3}{3 \times 10^{-2}} \\ \Rightarrow \quad & R & =57 \Omega \end{array}$
Hence, the correct answer is option: 'C'.