Question

The respective ratio of the resistance of 60W and 40W bulbs of the same rated voltage is:
1. 9 : 4
2. 3 : 2
3. 2 : 3
4. 4 : 9

Answer 1

Correct Answer - Option 3 : 2 : 3

Concept:

Electric Power:

• The rate of consumption of electrical energy is called Electric power.
• It is given as 

\(P = \frac{V^2}{R}\)

If the Potential difference is constant, Power is inversely proportional to resistance.

\(\implies P \propto \frac{1}{R}\) or 

Power × Resistance is constant

Calculation:

Now, Power of resistance 1 (R₁) = P₁ = 60 W

Now, Power of resistance 2 (R2) = P2 = 40 W

Now, P₁ R₁ = P₂. R₂

\(\implies \frac{R_1}{R_2} = \frac{P_2}{P_1}\)

\(\implies \frac{R_1}{R_2} = \frac{40}{60} = \frac{2}{3}\)

So, the required ratio is 2 : 3

The power in terms of current and resistance is given as 

P = I ² R

I is current

So, If the current would have been constant, the power would have been directly proportional to resistance.