Question

In the given circuit the reading of ideal voltmeter is $E/2$. The internal resistance of the battery is

• A. $1\Omega$
• B. $\frac{2}{3}\Omega$
• C. $\frac{2}{5}\Omega$
• D. $\frac{5}{2}\Omega$

Answer 1

The correct option is A $1\Omega$

The voltmeter reads the terminal p.d $\left(V\right)$ of the cell.
$i=\frac{2E}{r+3}$
$V=E-ir$
$V=E-\frac{2Er}{r+3}$
$\frac{E}{2}=\frac{3E-Er}{r+3}$ (Given $V=\frac{E}{2}$)
$\Rightarrow r+3=6-2r$
$3r=3$
$r=1\Omega$