Question
Two bulbs $$25\,W,220\,V$$ and $$100\,W,220\,V$$ are given. Which has higher resistance?
A.
$$25\,W$$ bulb
B.
$$100\,W$$ bulb
C.
Both bulbs will have equal resistance
D.
Resistance of bulbs cannot be compared
Answer :
$$25\,W$$ bulb
Solution :
Power of electric bulb, $$P = \frac{{{V^2}}}{R}$$
So, resistance of electric bulb, $$R = \frac{{{V^2}}}{P}$$
Given, $${P_1} = 25\,W,{P_2} = 100\,W,$$
$${V_1} = {V_2} = 220\,V$$
Therefore, for same Potential difference $$V,$$
$$R \propto \frac{1}{P}$$
Thus, we observe that for minimum power, resistance will be maximum and vice-versa.
Hence, resistance of $$25\,W$$ bulb is maximum and $$100\,W$$ bulb is minimum.