Six identical cells, each of emf 3 V and internal resistance of r, are connected in series to a 3 Ω resistance. If the net current flowing in the circuit is 2.0 A. The internal resistance of the cell is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $1Ω$
Given:
Number of cells $n = 6$
Each emf $E = 3 \, V \;\;\Rightarrow\;\; E_{total} = nE = 18 \, V$
Each internal resistance $= r \;\;\Rightarrow\;\; r_{total} = nr = 6r$
External resistance $R = 3 \, \Omega$
Current $I = 2 \, A$
Ohm’s law for the circuit:
$I = \frac{E_{total}}{R + r_{total}}$
$2 = \frac{18}{3 + 6r}$
$3 + 6r = \frac{18}{2} = 9$
$6r = 6 \;\;\Rightarrow\;\; r = 1 \, \Omega$
Answer: $1 \, \Omega$