Question

Two resistors of resistances, 100 Ω and 200 Ω are connected in parallel in an electrical circuit. The ratio of thermal energy developed in 100 Ω to that in 200 Ω in a given time is

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Answer 1

The Correct Option is B

When two resistors are connected in parallel, the voltage across each resistor is the same. The power dissipated as thermal energy in a resistor is given by the formula \( P = \frac{V^2}{R} \), where \( V \) is the voltage across the resistor and \( R \) is its resistance. 

Let the resistors be \( R_1 = 100 \, \Omega \) and \( R_2 = 200 \, \Omega \).

Since both resistors are in parallel, the voltage \( V \) across both is the same. The power \( P_1 \) for the 100 \(\Omega\) resistor is:

\( P_1 = \frac{V^2}{100} \)

And the power \( P_2 \) for the 200 \(\Omega\) resistor is:

\( P_2 = \frac{V^2}{200} \)

The ratio of thermal energy (power) developed in the 100 \(\Omega\) resistor to that in the 200 \(\Omega\) resistor is:

\(\text{Ratio} = \frac{P_1}{P_2} = \frac{\frac{V^2}{100}}{\frac{V^2}{200}} = \frac{200}{100} = 2:1\)

Thus, the ratio of thermal energy developed in the 100 \(\Omega\) resistor to that in the 200 \(\Omega\) resistor is 2:1.