Question

A $10\text{m}$ long wire of resistance $20\Omega$ is connected in series with a battery of emf $3\text{V}$ (negligible internal resistance) and a resistance of $10\Omega$. Find the potential gradient along the wire

• A. $3\text{V/m}$
• B. $0.2\text{V/m}$
• C. $0.1\text{V/m}$
• D. $0.3\text{V/m}$

Answer 1

The correct option is B $0.2\text{V/m}$

potential gradient $=\frac{\text{potential difference across}20\Omega }{\text{length of}20\Omega \text{wire}}$
$\varphi =\left(R_{\text{wire}}\right)\times \frac{I}{l}$
Current $I$
$=\frac{V}{(R_{\text{wire}}+R_{\text{external}})}=\frac{3}{(20+10)}=\frac{3}{30}=0.1\text{A}$
$\varphi =\frac{20\times 0.1}{10}=0.2\text{V/m}$