Question

An electric bulb is marked $100\mathrm{W}$ and $250\mathrm{V}$. Calculate the resistance of its filament. Two such bulbs are joined in series and then connected to $220\mathrm{V}$ mains. What is the power consumed by each bulb?

Answer 1

Step 1: Given data

Power marked by an electric bulb $\mathrm{P}=100\mathrm{W}$

Voltage marked on bulb $\mathrm{V}=250\text{volts}$

Applied potential is $220\text{volts}$

Step 2: Finding Resistance

We know that power, $\mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}}$ [Where V is the potential difference and R is the resistance]

So, $\mathrm{R}=\frac{{\mathrm{V}}^2}{\mathrm{P}}$

$R=\frac{{\left(250\right)}^2}{100}$

$\mathrm{R}=625\mathrm{\Omega }$

Step 3: Finding power consumed

Two identical bulbs are joined in series.

So, the potential drop across each bulb is equal.

Potential drop $=\frac{220}{2}$

Potential drop $=110\mathrm{V}.$

Power consumed by each bulb

$\mathrm{P}=\frac{{\mathrm{V}}^2}{\mathrm{R}}$

$$\begin{gathered} \mathrm{P}=\frac{{110}^2}{625} \\ P=19.36\mathrm{W} \end{gathered}$$

Hence, the power consumed by each bulb is $19.36\mathrm{W}$.