Question

two electric bulb of 40 w and 60 w connected to 120v line the ratio of there resistance wil be​

Answer 1

1:12 is your right answer to your question

Answer 2

Given:

Power of 1st electric bulb = 40W

Power of 2nd electric bulb = 60W

Potential across them = 120V

To find:

Ratio of resistances of two bulbs.

Solution:

Formula of power dissipated is-

$P = \frac{V^2}{R}= I^2R = VI$

here, P = power dissipated

        V = potential across the resistance

          I = current flowing across the resistance

In this question, to calculate resistance we will use the below formula,

$P = \frac{V^2}{R}$

therefore, $R = \frac{V^2}{P}$

Resistance of first electric bulb will be -

   $R_1 = \frac{V^2}{P_1}$

here, P₁ = 40W

         V = 120V

$R_1 = \frac{(120)^2}{40}$

R₁ = 360Ω

and, Resistance of second electric bulb is-

   $R_2 = \frac{V^2}{P_2}$

   $R_2 = \frac{(120)^2}{60}$

   R₂ = 240 Ω

Therefore, ratio of first resistance to the second resistance will be,

$\frac{R_1}{R_2} = \frac{360}{240}$

$\frac{R_1}{R_2} = \frac{3}{2}$

So, the ratio of resistance having power dissipated value 40W to the resistance having power dissipated value 60W is 3:2.