Question

two resistors of resistance R and 2R
 
are connected in parallel in an electric circuit. calculate the ratio of the electric power consumed by R and 2R

Answer 1

so P₁ = I²R₁
  and P₂ = I²r₂
so P₁/P₂ = R₁/R₂
           = R/2R
            = 1:2
answer

Answer 2

Answer:

The ratio of the electric power consumed by R and 2R is 2 : 1.

Explanation:

Power is consumed across the resistor when current flows through it.  

The formula for Power consumed, P = VI

P = V x (V/R) {because according to Ohm’s Law, V = IR}

$\bold{\mathrm{P}=\mathrm{V}^{2} / \mathrm{R}}$

So let $P_{1}$ = Power consumed across resistor $\mathrm{R}_{1}$

$\mathrm{P}_{2}=$ Power consumed across resistor $\mathrm{R}_{2}$

$\begin{array}{l}{\mathrm{R}_{1}=\mathrm{R}, \mathrm{R}_{2}=2 \mathrm{R}} \\ {\mathrm{P} 1 / \mathrm{P} 2=\frac{V^{2} / R_{1}}{V^{2} / R_{2}}=\mathrm{R}_{2} / \mathrm{R}_{1}=2 \mathrm{R} / \mathrm{R}=2 / 1}\end{array}$

Therefore ratio of the electric power consumed by R and 2R,$\bold{\mathrm{P}_{2} : \mathrm{P}_{1}=2 : 1}$