Two identical cells of emf 2 V each joined in parallel provide supply to an external circuit containing two resistors of $20 \Omega$ each joined in parallel. A very high resistance voltmeter reads the terminal voltage of the cells to be 1.6 V. The internal resistance of each cell is:

$5 \Omega$

The correct answer is Option (4) → $5 \Omega$

EMF of each cell, E = 2V$

Terminal voltage, $V=1.6V$

Resistors are connected in parallel and their net resistance is -

$R_{eq}=\frac{R}{2}=\frac{20}{2}=10Ω$

Voltage across the external circuit = $1.6V$

$∴I_{ext}=\frac{V}{R_{eq}}=\frac{1.6}{10}=0.16A$

Let $r$ be the internal resistance of each cell. The total internal resistance for each cell is -

$r_{total}=\frac{r}{2}$

and,

$I_{total}=I_{ext}=0.16A$

By using Kirchhoff's Voltage law -

$E-I_{total}.r_{total}=V$

$2V-0.16A.\frac{r}{2}=1.6V$

$⇒r=5 \Omega$