Question

Three equal resistances each of 3$\Omega$ are in series and connected to a cell of internal resistance one ohm. If these resistances are in parallel and connected to the same cell, then the ratio of the respective currents through the electric circuits in the two cases is

• A. 1/8
• B. 1/7
• C. 1/5
• D. 1/3

Answer 1

Answer: (C)

1/5

If the resistances are in series then total resistance in the circuit is $(3+3+3)+1=10$ ohm.
So the current in the circuit is $I_s=\frac{V}{10}$A. Where, $V$ is the battery voltage.
Again, if the resistances are in parallel then total resistance in the circuit is $\left(3||3||3\right)+1=2$ ohm.
So the current in the circuit is $I_p=\frac{V}{2}$ A. Where, $V$ is the battery voltage. So, $\frac{I_s}{I_p}=\frac{1}{5}$.