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

Step 1: Understanding the Concept:
Thermal energy (Heat) developed in a resistor is given by Joule's Law of heating.
In a parallel connection, the potential difference (\(V\)) across all resistors is the same.
Key Formula or Approach:
The formula for heat produced in time \(t\) is:
\[ H = \frac{V^2}{R} t \]
For a parallel combination where \(V\) and \(t\) are the same:
\[ H \propto \frac{1}{R} \]
Step 2: Detailed Explanation:
Let \(H_1\) be the heat produced in \(R_1 = 100\) \(\Omega\) and \(H_2\) be the heat produced in \(R_2 = 200\) \(\Omega\).
Using the inverse relationship:
\[ \frac{H_1}{H_2} = \frac{R_2}{R_1} \]
Substitute the values:
\[ \frac{H_1}{H_2} = \frac{200}{100} \]
\[ \frac{H_1}{H_2} = \frac{2}{1} \]
Thus, the ratio of thermal energy is \(2 : 1\).
Step 3: Final Answer:
The ratio of thermal energy developed is \(2 : 1\).