Question 184 of 380

Two identical cells each of emf $1.5V$ are connected in parallel across a parallel combination of two resistors each of resistance $20\Omega$. A voltmeter connected in the circuit measures $1.2V$. The internal resistance of each cell is :

A$2.5\Omega$B$4\Omega$C$5\Omega$D$10\Omega$

Show answer and solution▾

Answer: (C) $5\Omega$

Equivalent resistance of the parallel $20\Omega$ branches will be $10\Omega$.
Equivalent EMF of the two branches which are in parallel will be, $=\dfrac{\dfrac{1.5}{r}+\dfrac{1.5}{r}}{\dfrac{1}{r}+\dfrac{1}{r}}=1.5V$ and the equivalent internal resistance for same branches will be, $\dfrac{r}{2}$.
For loop containing voltmeter and $10\Omega$ resistor, $1.2-10i=0\Rightarrow i=0.12A$.
Reading of voltmeter should be,
$1.2=1.5-i\left(\dfrac{r}{2}\right)\Rightarrow i\left(\dfrac{r}{2}\right)=0.3\Rightarrow r=\dfrac{0.6}{i}=\dfrac{0.6}{0.12}=5\Omega$