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:
Answer & explanation
Correct answer: option 4
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 -
$E-I_{total}.r_{total}=V$
$2V-0.16A.\frac{r}{2}=1.6V$
$⇒r=5 \Omega$