Question

There are a $25\, W -220\, V$ bulb and a $100\, W-220\, V$ line. Which electric bulb will glow more brightly?

• A. 25W bulb
• B. 100W bulb
• C. Both will have equal incadescene
• D. Neither 25 W nor 100 W bulb will give light

Answer 1

Answer: (A)

25W bulb

Answer 2

Since power $P$ is given by $P=V^{2} / R$, so $R=V^{2} / P$ For the first bulb, $R_{1}=\left(\frac{V^{2}}{P_{1}}\right)=\left[\frac{(220)^{2}}{25}\right]=1936\, \Omega$ For the second bulb, $R_{2}=\left(\frac{V^{2}}{P_{2}}\right)=\left[\frac{(220)^{2}}{100}\right]=484\, \Omega$ Current in series combination is the same in the two bulbs and current $i$ is given by $i =\frac{V}{R_{1}+R_{2}}=\frac{220}{1936+484}$ $=\frac{220}{2420}=\frac{1}{11} A$ If the actual powers in the two bulbs be $P_{1}$ and $P_{2}$ then $P_{1}'=i^{2} R_{1}=\left(\frac{1}{11}\right)^{2} \times 1936=16\, W$ and $P_{2}'=i^{2} R_{2}=\left(\frac{1}{11}\right)^{2} \times 484=4\, W$ Since $P_{1}' >P_{2}', 25\, W$ bulb will glow more brightly.