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 in 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

The correct option is D $20$ watts

Rating of the resistor : $P=320W$ and $V=220$ volts
Resistance of the resistor $R=\frac{V^2}{P}=\frac{{220}^2}{320}$
When these are connected in series, voltage across each other $V_s=\frac{110}{2}=55$ volts
Thus power generated in each resistor $P_s=\frac{V_s^2}{R}$
$⟹P_s=\frac{{55}^2}{\frac{{220}^2}{320}}=\frac{320}{4^2}=20W$