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,
$P^{{}^{\prime }}=\frac{{\left(V^{\prime }\right)}^2}{R}=\frac{{\left(\frac{110}{2}\right)}^2}{R}=\frac{110\times 110}{2\times 2}\times \frac{P}{V^2}$
$=\frac{110\times 110}{2\times 2}\times \frac{320}{220\times 220}$
$=\frac{1}{4}\times \frac{1}{4}\times 320=20$ watts.