JEE Main 2022 — Current Electricity Question with Solution

Equivalent resistance of the parallel $20 \mathrm{\Omega }$ branches will be $10 \mathrm{\Omega }$.

Equivalent EMF of the two branches which are in parallel will be, $=\frac{\frac{1.5}{r}+\frac{1.5}{r}}{{\displaystyle \frac{1}{r}}+{\displaystyle \frac{1}{r}}}=1.5 \mathrm{V}$ and the equivalent internal resistance for same branches will be, $\frac{r}{2}$.

For loop containing voltmeter and $10 \mathrm{\Omega }$ resistor, $1.2-10i=0 \Rightarrow i=0.12 \mathrm{A}$.

Reading of voltmeter should be,

$1.2=1.5-i\left(\frac{r}{2}\right) \Rightarrow i\left(\frac{r}{2}\right)=0.3 \Rightarrow r=\frac{0.6}{i}=\frac{0.6}{0.12}= 5 \mathrm{\Omega }$