Question

Two resistors of $10$ and $20$ are connected in parallel to a battery. The ratio of the power dissipated by the $10$ resistor to the power dissipated by the $20$ resistor is

• A. $1:2$
  
• B. $1:4$
  
• C. $2:1$
  
• D. $4:1$
  

Answer 1

Answer: (C)

$2:1$

Power dissipated by a resistor $P=\frac{V^2}{R}$

As the two resistors are connected in parallel across a battery, thus both have same potential difference.

$⟹$ $P\propto \frac{1}{R}$

Given : $R_1=10\Omega$ and $R_2=20\Omega$

Ratio of power dissipated $\frac{P_1}{P_2}=\frac{R_2}{R_1}$

OR $\frac{P_1}{P_2}=\frac{20}{10}$

$⟹$ $P_2:P_1=2:1$