Question

Two bulbs when connected in parallel to a source take $100W$ 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
$P^{\prime }=\frac{{\left(\frac{V}{2}\right)}^2}{R}+\frac{{\left(\frac{V}{2}\right)}^2}{R}=\frac{V^2}{2R}$
$\therefore P^{\prime }=\frac{P}{2}=\frac{100}{2}=$ $50W$