Question

Two bulbs when connected in parallel to a source take $100 \, W$ each. The total power consumed when they are connected in series with the same source is

• A. $25W$
• B. $50W$
• C. $100W$
• D. $200W$

Answer 1

Answer: (B)

Let $R$ be the resistance of each bulb.
We have $P=\frac{V^{2}}{R}$
or $R=\frac{V^{2}}{P}=\frac{V^{2}}{100}$
When the bulbs are connected in series, the voltage across each of them is . Hence, the total power consumed is
$ \, P^{′}=\frac{\left( \, \frac{V}{2}\right)^{2}}{R}+\frac{\left( \, \frac{V}{2}\right)^{2}}{R}=\frac{V^{2}}{2 R}$
$\therefore P^{′}=\frac{P}{2}=\frac{100}{2}=$ $50W$