Question

A $50W$ bulb is in series with a room heater and the combination is connected across the mains. To get max. heater output, the $50W$ bulb should be replaced by

• A. $20W$
• B. $10W$
• C. $100W$
• D. $200W$

Answer 1

The correct option is D

$200W$

Step 1: Given data

Power of the bulb $P=50W$

Let $i$ be the current.

Let $V$ be the voltage.

Let $R_1$ be the resistance of the bulb.

Let $R_2$ be the resistance of the heater.

Step 2: Relation between heat and resistance

We know that heating in a circuit is given as

$H=i^{2}R={\left(\frac{V}{R_1+R_2}\right)}^2{R}_2$

We can see that,

$H\propto \frac{1}{R_1}$.

Therefore to get a maximum heating output, the $50W$ bulb should be replaced by the highest-rated power bulb i.e. $200W$.

Hence, the correct answer is option (D).