JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Current Electricity

Two identical cells, when connected either in parallel or in series gives same current in an external resistance

5Ω

. The internal resistance of each cell will be

____

Ω

Answer: 5

Solution

In series the two cells give a current

i_{s} = \frac{2 ε}{R + 2 r}

, while in parallel they give

i_{p} = \frac{ε}{R + \frac{r}{2}}

, with

R = 5 Ω

. Equating the currents,

\frac{2 ε}{5 + 2 r} = \frac{ε}{5 + \frac{r}{2}}

, so

2 (5 + \frac{r}{2}) = 5 + 2 r

, which gives

10 + r = 5 + 2 r

. The internal resistance of each cell is therefore

r = 5 Ω

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Integer answer