Question

The ratio of the resistance of two bulbs is 1:2. When the two bulbs are connected in series then the ratio of the power consumed by each bulb is:
1. 1:4
2. 4:1
3. 1:2
4. 2:1

Answer 1

Correct Answer - Option 3 : 1:2

CONCEPT:

Electric power:

• The rate at which the electric energy is dissipated or consumed is termed as electric power.
• The electric power is given as,

\(⇒ P=IV=I^{2}R=\frac{V^{2}}{R}\)

Where P = electric power, V = voltage, I = current and R = resistance

CALCULATION:

Given \(\frac{R_{1}}{R_{2}}=\frac{1}{2}\)

Where R₁ and R₂ are the resistance of the bulbs

• We know that in series connection the current in both the bulbs will be equal.

⇒ I₁ = I₂ = I     -----(1)

• The power consumed by a resistance R in the circuit is given as,

⇒ P = I² R     -----(2)

• So the power consumed by the bulb of resistance R₁ is given as,

⇒ P₁ = I2 R₁     -----(3)

• And the power consumed by the bulb of resistance R2 is given as,

⇒ P2 = I2 R2     -----(4)

By dividing equation 3 and equation 4,

\(\Rightarrow \frac{P_{1}}{P_{2}}=\frac{I^2R_{1}}{I^2R_{2}}\)

\(\Rightarrow \frac{P_{1}}{P_{2}}=\frac{R_{1}}{R_{2}}\)

\(\Rightarrow \frac{P_{1}}{P_{2}}=\frac{1}{2}\)

• Hence, option 3 is correct.