Question

Two bulbs marked 200 watt-250 volts and 100 watt-250 volts are joined in series to 250 volts supply. Power consumed in circuit is:

• A. 100 watt
• B. 33 watt
• C. 300 watt
• D. 67 watt

Answer 1

The correct option is D

67 watt

Power dissipated in a resistor is:
$P=\frac{V^2}{R}$

Given:
Rated power of the first bulb, $P_1=200watts$
Resistance of the 1st bulb is:
$R_1=\frac{{250}^2}{200}\Omega$
$R_1=\frac{625}{2}\Omega$

Rated power of the second bulb $P_2=100watts$
Resistance of the 2nd bulb is:
$R_2=\frac{{250}^2}{100}$
$R_2=625\Omega$

Total resistance of the circuit when the bulbs are connceted in series is:
$R=R_1+R_2$
$R=\frac{625}{2}+625=\frac{1875}{2}\Omega$

Operating voltage, $V=250volts$
Therefore, total power consumed in the circuit:
$P=\frac{V^2}{R}$
$P=\frac{{250}^2}{1875/2}$
$P=66.67W$