Question

An electric lamp whose resistance is 10 ohm and a conductor of 2-ohm resistance are connected in series with a 6 V battery. The total current through the circuit and the potential difference across the electric lamp are?
A. 3.6 A, 6 V
B. 0.5 A, 5 V
C. 2 A, 0.2 V
D. 0.3 A, 3V

Answer 1

Hint: We are given with the resistance of the lamp and the resistance of the conductor. They both are connected in series and so we can find the equivalent resistance using the series combination of the resistance. They are connected to an external source of EMF. In order to find the individual voltage and current across the lamp and the conductor we can make use of Ohm’s law to find the total current in the circuit.

Complete step by step answer:
Resistance of lamp ${{R}_{1}}=10\Omega $
Resistance of the conductor ${{R}_{2}}=2\Omega $
They both are connected in series, so equivalent resistance $R=10+2=12\Omega $
Now potential difference of the battery is 6 V. using Ohm’s law $V=iR$
$i=\dfrac{V}{R}$
$\Rightarrow i=\dfrac{6}{12}$
$\therefore i=0.5A$

Since in series combination the current remains the same, so current through both the lamp and conductor is 0.5 A. Now, potential difference across the lamp, we apply Ohm’s law for lamp:
$V=iR$
$\Rightarrow V=0.5\times 10$
$\therefore V=5V$
Thus, the current in the circuit comes out to be 0.5 a and the potential difference across the lamp is 5 V.

So, the correct option is B.

Note: We should always remember that in a series combination the current remains the same while in a parallel combination the voltage remains same. Also, ohm’s law does not hold for all the conductors and under all conditions of temperature and pressure. Ohm’s law can be applied to any conductor which is Ohmic and follows Ohm's law at all conditions of temperature and pressure.