Power Dissipation Calculation Using Voltage and Resistance

This problem requires calculating the electrical power dissipated by a resistor given the voltage applied across it and its resistance value. We can use a fundamental formula from electrical theory to find the solution.

Understanding the Concepts

Electrical power is the rate at which electrical energy is transferred by an electric circuit. When voltage is applied across a resistor, energy is dissipated, typically as heat. The relationship between power (P), voltage (V), and resistance (R) is defined by the following formula:

• Power (P) is measured in Watts (W).
• Voltage (V) is measured in Volts (V).
• Resistance (R) is measured in Ohms (Ω).

Power Formula

The formula to calculate power dissipated in a resistor when voltage and resistance are known is:

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

Applying the Formula

Given the values:

• Voltage, V = 100 V
• Resistance, R = 20 Ω

Substitute these values into the power formula:

1. Square the voltage: V^2 = (100 \text{ V})^2 = 10000 \text{ V}^2
2. Divide the squared voltage by the resistance: P = \frac{10000 \text{ V}^2}{20 \text{ Ω}}
3. Calculate the result: P = 500 \text{ W}

Result

The power dissipated by the resistance is 500 Watts.

Analysis of Options

Let's review the given options:

• Option 1: 500 Watts - This matches our calculated value.
• Option 2: 2000 Watts - Incorrect.
• Option 3: 200 Watts - Incorrect.
• Option 4: 5 Watts - Incorrect.