Question

Two electric bulbs $\text{A}$ and $\text{B}$ are rated $60\text{W}$ and $100\text{W}$ respectively. If they are connected in parallel to the same source, then
$($Assume bulb $\text{A}$ and $\text{B}$ have same voltage rating.)

• A. Both the bulbs draw the same current.
• B. Bulb $\text{A}$ draws more current than bulb $\text{B}$.
• C. Bulb $\text{B}$ draws more current than bulb $\text{A}$.
• D. Current drawn in the bulbs are in the ratio of their resistances.

Answer 1

The correct option is C Bulb $\text{B}$ draws more current than bulb $\text{A}$.

Given,
$P_A=60\text{W};P_B=100\text{W}$

We know that current flowing through the bulb is given by :

$I=\frac{P}{V}$

$\because$ Both the bulbs are connected in parallel, therefore potential drop $\left(V\right)$ across both the bulbs will be same. So, we get

$I\propto P$

$\therefore \frac{I_A}{I_B}=\frac{P_A}{P_B}$

Since, power of bulb $\text{B}$ is greater than that bulb $\text{A}$, therefore bulb $\text{B}$ draws more current than bulb $\text{A}$.

Hence, option $\left(c\right)$ is correct.

Key concept When bulbs are connected in Parallel to the voltage source $V$ Then potential drop is same across them. $P=\frac{V^2}{R}$ $R=\frac{(V_{rating}{)}^2}{P_{rating}}$ $\therefore P=\frac{V^2}{V_{rating}^2/P_{rating}}$ $\Rightarrow P=\frac{V^2{P}_{rating}}{V_{rating}^2}=VI$ $\therefore P\propto I;P\propto P_{rating}$ So, in parallel connection, bulb having higher power rating will consume more power and more current will flow through it.