Question

When a current of $(2.50\pm 0.5)A$ flows through a wire, it develops a potential difference of $(20\pm 1)V$. The resistance of the wire is :

• A. $(8\pm 2)\Omega$
• B. $(10\pm 3)\Omega$
• C. $(18\pm 4)\Omega$
• D. $(20\pm 6)\Omega$

Answer 1

The correct option is A $(8\pm 2)\Omega$

Given that current of $2.50\pm 0.5$ A flows across a wire of potential difference $20\pm 1V$.
$V=IR$ or $R=\frac{V}{I}=\frac{20}{2.5}=8\Omega$

$\Rightarrow \frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta I}{I}$

$=\frac{1}{20}+\frac{0.5}{2.5}=0.05+0.2=0.25$

$\Delta R=0.25\times 8=2$
Now, we have resistance with limits of error $=8\pm 2\Omega$