Question

Two identical bulbs are marked $100W,220V.$ The bulbs are connected in series to a $100V$ electric supply. What is the power consumed by each bulb?

Answer 1

Step 1: Given,

For bulb:

$$\begin{gathered} Power{P}_1=100\hspace{0.17em}W \\ Voltage{V}_1=220V \end{gathered}$$

The voltage of the electric supply is $V_2=100\text{volts}$

Step 2: Find the power consumed by each bulb

Resistance for each bulb is,

$Resis\tan ce\left(R\right)=\frac{{V_1}^2}{P_1}$ [Where V= potential, P= power, and R= Resistance]

Now put the given value in the above formula

$$\begin{gathered} =\frac{220\times 220}{100} \\ =484ohms. \end{gathered}$$

$\because$ Bulb identical and connected in series so, the potential of each bulb

$V_3=\frac{V_2}{2}$

$V_3=\frac{100}{2}$

$V_3=50\text{volts}$

Power consumed by each bulb

$$\begin{gathered} P=\frac{{V_3}^2}{R} \\ =\frac{50\times 50}{484} \end{gathered}$$

$=5.16\text{watts}$

Hence, the power consumed by each bulb is $5.16\text{watts}$.