Question

A resistor develops 800 J of thermal energy in 20 s on applying a potential difference of 20 V. Its resistance is

• A. 20 \(\Omega\)
• B. 10 \(\Omega\)
• C. 40 \(\Omega\)
• D. 0.5 \(\Omega\)

Hint:

Remember the three main formulas for electrical power: \(P = VI\), \(P = I^2R\), and \(P = V^2/R\). Choose the formula that directly uses the quantities given in the problem (here, V and E/t) to avoid unnecessary intermediate calculations (like finding the current I).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem involves the heating effect of electric current, also known as Joule heating. When a potential difference is applied across a resistor, electrical energy is converted into thermal energy. We are given the energy, time, and voltage, and we need to find the resistance.

Step 2: Key Formula or Approach:
The electrical power \(P\) dissipated in a resistor is the rate at which energy is converted. \[ P = \frac{E}{t} \] where \(E\) is the energy and \(t\) is the time.
The power dissipated in a resistor can also be expressed in terms of voltage \(V\) and resistance \(R\): \[ P = \frac{V^2}{R} \] By combining these two formulas, we can solve for the resistance \(R\).

Step 3: Detailed Explanation:
Given data:
Thermal energy, \(E = 800 \, \text{J}\).
Time, \(t = 20 \, \text{s}\).
Potential difference, \(V = 20 \, \text{V}\).
Calculation:
First, calculate the power \(P\) dissipated by the resistor: \[ P = \frac{E}{t} = \frac{800 \, \text{J}}{20 \, \text{s}} = 40 \, \text{W} \] Now, use the power formula involving voltage and resistance to find \(R\): \[ P = \frac{V^2}{R} \] Rearranging for \(R\): \[ R = \frac{V^2}{P} \] Substitute the given values: \[ R = \frac{(20 \, \text{V})^2}{40 \, \text{W}} = \frac{400 \, \text{V}^2}{40 \, \text{W}} = 10 \, \Omega \]

Step 4: Final Answer:
The resistance of the resistor is 10 \(\Omega\).