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 ______ $$\Omega$$.

The voltmeter (10 kΩ) is connected in parallel with the unknown resistance R, so the measured V-I relation corresponds to the equivalent resistance of the parallel combination.

From the graph:

At V = 8 V, I = 4 mA

So equivalent resistance:

$$Req=\frac{V}{I}=\frac{8}{4\times10^{-3}}=2000Ω=2kΩ$$

Now,

Req=R∥10 kΩ

$$\frac{1}{2000}=\frac{1}{R}+\frac{1}{10000}$$

Solve:

$$\frac{1}{R}=\frac{1}{2000}-\frac{1}{10000}=\frac{5-1}{10000}=\frac{4}{10000}=\frac{1}{2500}$$

R=2500 Ω=2.5 kΩ