Question

Two electric resistors have equal values of resistance $R$. Each can be operated with a power of $320$ watts $( W )$ at $220$ volts. If the two resistors are connected in series to a $110$ volts electric supply, then the power generated in each resistor is

• A. 90 watts
• B. 80 watts
• C. 60 watts
• D. 20 watts

Answer 1

Answer: (D)

Power, $ P =\frac{V^{2}}{R} $
$R =\frac{V^{2}}{P} $
Here, $P=320$ watts
$V=220$ volts
When the resistors are connected in series, then power developed across each resistor,
$ P^{'} =\frac{\left(V^{\prime}\right)^{2}}{R}=\frac{\left(\frac{110}{2}\right)^{2}}{R}=\frac{110 \times 110}{2 \times 2} \times \frac{P}{V^{2}} $
$=\frac{110 \times 110}{2 \times 2} \times \frac{320}{220 \times 220}$
$=\frac{1}{4} \times \frac{1}{4} \times 320=20 $ watts.