Question

One electric bulb is rated 60W - 240 V and other 40 W-240V. Which bulb has a higher resistance and how many times?​

Answer 1

Answer: R₂ is the higher resistance with 1.5 times more than R₁

Given:

$\sf\text{Power of the first bulb}(P_1)=60\:W$

$\sf\text{Power of the second bulb}(P_2)=40\:W$

$\sf\text{Voltage of the first and second bulb}(V)=240\:V$

To find:

$\sf\text{The bulb which has higher resistance and how many times.}$

Explanation:

$\sf\textbf{``Power is the amount of energy transferred or converted per unit time."}$

$\sf\text{We know that,}$

$\boxed{\sf\text{P=VI}}$

$\sf\text{Therefore,}$

$\sf \quad \quad \: P=\frac{V^2}{R}$

$\sf or,\boxed{\:R=\frac{V^2}{P}}$

$\sf\text{According to the question,}$

$\sf\ R_1=\frac{V^2}{P_1} =\frac{240^2}{60}=960 \Omega$

$\sf\ R_2=\frac{V^2}{P_2} =\frac{240^2}{40}=1440 \Omega$

$\sf Now,$

$\sf \frac{R_2}{R_1}=\frac{1440}{960}=1.5$

$\textbf{\boxed{\sf R_2=1.5\ R_1}}$

$\sf\textbf{Therefore, the higher resistance is\:} R_2 \sf\textbf{\:and it is 1.5 times more than\:}R_1$