Question

There are 4 resistors, each having the same resistance of 4 ohms. These are first connected in series with a cell of internal resistance 2 ohms. Then, they are connected in parallel to the same cell. Find the ratio of the respective currents in the two cases.

(a) 1:8

(b) 1:7

(c) 1:6

(d) 6:1

This question was posed to me in unit test.

My doubt stems from Current Electricity in portion Current Electricity of Physics – Class 12

Answer 1

The correct choice is (c) 1:6

For explanation I would say: When the resistors are connected in series:

RS = 4 + 4 + 4 + 4 = 16 ohms

They are connected to a cell of internal resistance of 2 ohms, so current (I1) = \(\frac {e}{R_S}\) + r                                                                                                                                                                                                         = \(\frac {e}{6}\) + 2                                                                                                                                                                                                     = \(\frac {e}{18}\)

When the resistors are connected in parallel:

\(\frac {1}{R_P} = \frac {1}{4} + \frac {1}{4} + \frac {1}{4} + \frac {1}{4}\) = 1  →  RP = 1

The current through the circuit (I2) = \(\frac {e}{1+2}\)

= \(\frac {e}{3}\)

Ratio of both the currents = \(\frac {I_1}{I_2} = \frac {\frac {e}{18}}{\frac {e}{3}} = \frac {1}{6}\)  →  1:6