Question

When current flows through a long solenoid having $1000$ turns per metre, the magnetic field at its centre is found to be $2\pi \times {10}^{-4}\text{T}$. What would be the resistance of the solenoid if it is connected across $6\text{V}$ battery ?

• A. $3\Omega$
• B. $6\Omega$
• C. $12\Omega$
• D. $15\Omega$

Answer 1

The correct option is C $12\Omega$

Given:
$n=1000;B=2\pi \times {10}^{-4}\text{T};V=6\text{V}$

The magnetic field at the centre of long solenoid will be

$B={\mu }_{0}ni$

$2\pi \times {10}^{-4}=4\pi \times {10}^{-7}\times 1000\times i$

$\therefore i=0.5\text{A}$

Now, using $V=iR$

$6=0.5\times R$

$\therefore R=12\Omega$

Hence, option $\left(c\right)$ is correct.