Question

Assertion :A $60W$ bulb is connected in series with a room heater and combination is connected across the mains. If the $60W$ is replaced by a $100W$ bulb, the heat produced by the heater will be more. BECAUSE Reason: The heat produced in inversely proportional to resistance when the resistances are connected in series across the mains.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

The resistance ($R_1$) of the $60W$ bulb is higher than resistance ($R_2$) of the $100W$ bulb. If $R$ is the resistance of the heater and $V$ the voltage of the mains, the currents through the $60W$ bulb and $100W$ respectively are
$I_1=\frac{V}{R+R_1};I_2=\frac{V}{R+R_2}$
since $R_1>R_2;I_2>I_1$. Since th eheater and the bulb are connected in series, the current through the bulb = current through the heater. Now, heat produced by the heater is proportional to the square of the current flowing through it.