Question

To determine the resistance (R) of a wire, a circuit is designed below, The V-I characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of R is ………… \(\Omega\). 

Answer 1

Correct answer is :  2500  

Req \(=\frac{10^{4} \mathrm{R}}{10^{4}+\mathrm{R}}\)

\(\mathrm{E}=4 \mathrm{~V}, \mathrm{I}=2 \mathrm{mA}\)

\(\mathrm{I}=\frac{\mathrm{E}}{\operatorname{Req}} \Rightarrow 2 \times 10^{-3}=\frac{4\left(10^{4}+\mathrm{R}\right)}{10^{4} \mathrm{R}}\)

\(\Rightarrow 20 \mathrm{R}=40000+4 \mathrm{R}\)

\(16 \mathrm{R}=40000\)

\(\mathrm{R}=2500 \Omega\)