Question

If resistance of the filament increases with temperature, what will be power dissipated in a $220V-100W$ lamp when connected to $110V$ power supply

• A. None of the above
• B. $<25W$
• C. $25W$
• D. $>25W$

Answer 1

The correct option is D $>25W$

Step 1: When resistance does not vary with temperature

Power dissipated by lamp,

$P=\frac{V^2}{R}$

If $R$ remains constant then,

$\frac{P_1}{P_2}={\left(\frac{V_1}{V_2}\right)}^2$

Given,

$P_1=100W,V_1=220V,V_2=110V$

Then,

$\Rightarrow P_2={\left(\frac{V_2}{V_1}\right)}^2\times P_1={\left(\frac{110}{220}\right)}^2\times 100$

$\Rightarrow P_2=25W$

Step 2: When resistance vary with temperature

On decreasing the voltage, heat developed in the filament will also decrease, due to which its resistance also decreases.

And as,

$P\propto \frac{1}{R}$

$\therefore$ Power consumed by the lamp will increase

Hence, it would be greater than $25W$.

Hence, option (C) is correct.