Two cells of emf $1\ \text{V}$ and $2\ \text{V}$ and internal resistance $2\ \Omega$ and $1\ \Omega$, respectively, are connected in series with an external resistance of $6\ \Omega$. The total current in the circuit is $I_1$. Now the same two cells in parallel configuration are connected to the same external resistance. In this case, the total current drawn is $I_2$. The value of $\left(\dfrac{I_1}{I_2}\right)$ is $\dfrac x3$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 4
**Series** (emfs aiding): $I_1 = \dfrac{1 + 2}{2 + 1 + 6} = \dfrac13\ \text{A}$.
**Parallel** (like terminals together): the equivalent cell has
$$\varepsilon_{eq} = \frac{\frac{1}{2} + \frac{2}{1}}{\frac12 + \frac11} = \frac{5}{3}\ \text{V},\qquad r_{eq} = \frac{2\times1}{2 + 1} = \frac23\ \Omega$$
$$I_2 = \frac{5/3}{2/3 + 6} = \frac{5/3}{20/3} = \frac14\ \text{A}$$
$$\frac{I_1}{I_2} = \frac{1/3}{1/4} = \frac43 \Rightarrow x = 4$$
Solution by Sreeraj P, M.Sc Physics