question_answer

Two bulbs 25 W, 220 V and 100 W, 220 V are given. Which has higher resistance?                  [AIPMT 2000]

A)  25 W bulb

B)                   100 W bulb C)  Both bulbs will have equal resistance        D)  Resistance of bulbs cannot be compared Correct Answer: A Solution : [a] Power of electric bulb

\[P=\frac{{{V}^{2}}}{2R}\]

So, resistance of electric bulb

\[R=\frac{{{V}^{2}}}{P}\]

Given, \[{{P}_{1}}=25\text{ }W,{{P}_{2}}=100\text{ }W,\text{ }{{V}_{1}}={{V}_{2}}=220\,V\]

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.