Question

Two bulb of 500w and 200w rated at 250v will have resistance ratio as ?​

Answer 1

2:5 is the correct answer

Answer 2

Answer:

$\dfrac{R_1}{R_2}=\dfrac{2}{5}$

Explanation:

It is given that,

Power of one bulb, $P_1=500\ W$

Power of other bulb, $P_2=200\ W$

Voltage, V = 250 V

The power of an electrical appliance is given by :

$P_1=\dfrac{V^2}{R_1}$

$R_1=\dfrac{V^2}{P_1}$

$R_1=\dfrac{(250)^2}{500}$...........(1)

The power of other bulb is given by :

$P_2=\dfrac{V^2}{R_2}$

$R_2=\dfrac{V^2}{P_2}$

$R_1=\dfrac{(250)^2}{200}$..............(2)

So, the resistance ratio is given by :

$\dfrac{R_1}{R_2}=\dfrac{\dfrac{(250)^2}{500}}{\dfrac{(250)^2}{200}}$

$\dfrac{R_1}{R_2}=\dfrac{2}{5}$

So, the resistance ratio is 2:5. Hence, the correct option is (c).