Understanding Power Dissipation in Resistors

This question asks us to determine the power dissipated in a resistor. Power dissipation in a resistor is the rate at which electrical energy is converted into heat due to the resistance.

Key Concepts for Resistor Power Calculation

To calculate the power dissipated in a resistor, we need to know its resistance and either the voltage across it or the current flowing through it. There are standard formulas derived from Ohm's Law and the definition of power.

• Resistance (R): Measured in ohms (\(\Omega\)). It opposes the flow of electric current.
• Current (I): Measured in amperes (A). It is the flow of electric charge.
• Power (P): Measured in watts (W). It is the rate at which energy is transferred or dissipated.

Formulas for Power Dissipation

There are three common formulas to calculate power (P) in a resistor:

• \(P = VI\): Power equals Voltage multiplied by Current.
• \(P = I^2 R\): Power equals Current squared multiplied by Resistance. This formula is directly applicable when Current (I) and Resistance (R) are known.
• \(P = \frac{V^2}{R}\): Power equals Voltage squared divided by Resistance. This formula is useful when Voltage (V) and Resistance (R) are known.

All these formulas are related through Ohm's Law, which states \(V = IR\).

Calculating Power in the 5-ohm Resistor

We are given the following information:

• Resistance of the resistor (\(R\)) = 5 ohms (\(5 \, \Omega\))
• Current flowing through the resistor (\(I\)) = 2 A (\(2 \, \text{A}\))

Since we have the current (\(I\)) and the resistance (\(R\)), the most direct formula to use is \(P = I^2 R\).

Step-by-Step Power Calculation

1. Identify the given values: \(R = 5 \, \Omega\), \(I = 2 \, \text{A}\).
2. Choose the appropriate formula: \(P = I^2 R\).
3. Substitute the given values into the formula: \(P = (2 \, \text{A})^2 \times 5 \, \Omega\).
4. Calculate the square of the current: \((2 \, \text{A})^2 = 4 \, \text{A}^2\).
5. Multiply the squared current by the resistance: \(P = 4 \, \text{A}^2 \times 5 \, \Omega\).
6. Perform the multiplication: \(P = 20 \, \text{W}\).

The power dissipated in the 5-ohm resistor carrying a 2 A current is 20 W.

Summary of Power Dissipation Calculation

Using the formula \(P = I^2 R\), we calculated the power dissipated in the 5-ohm resistor with a 2 A current.

Revision Table: Electrical Quantities and Formulas

Here is a quick table summarizing the related electrical quantities and the formulas connecting them.

Additional Information: Why Resistors Dissipate Power?

Resistors dissipate electrical power because they oppose the flow of charge. As electrons move through the resistive material, they collide with atoms in the material. These collisions transfer kinetic energy from the electrons to the atoms, causing the atoms to vibrate more vigorously. This increased vibration is observed as heat. The power dissipated is the rate at which this electrical energy is converted into thermal energy.

Understanding power dissipation is crucial in circuit design. Components must be chosen with appropriate power ratings to avoid overheating and damage. If a resistor is forced to dissipate more power than it is designed for, its temperature can rise excessively, leading to changes in its resistance, or even permanent failure.

The power dissipation depends on both the resistance and the current (or voltage). Higher resistance or higher current (or voltage) leads to greater power dissipation and thus more heat generation. This principle is used in heating elements like those found in electric heaters, toasters, and hair dryers, where resistance is specifically designed to generate a significant amount of heat when current flows.