Power Rating of a Resistor. The power rating of a resistor is the maximum power the resistor can safely dissipate without too great a rise in temperature and hence damage to the resistor. (b) A 9.0-kΩ resistor is to be connected across a 120-V potential difference. What power rating is required?

Verified step by step guidance

1. Identify the given values: Resistance (R) = 9.0 kΩ = 9000 Ω, Voltage (V) = 120 V.
2. Recall the formula for power dissipated by a resistor, P = V^2 / R, where P is the power, V is the voltage across the resistor, and R is the resistance.
3. Substitute the given values into the power formula: P = (120 V)^2 / 9000 Ω.
4. Calculate the value inside the parentheses first, which is the square of the voltage, (120 V)^2.
5. Divide the result from the previous step by the resistance to find the power rating required for the resistor.

Key Concepts

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed as V = IR, which is fundamental for analyzing electrical circuits and calculating current, voltage, or resistance when two of the three quantities are known.

Power in Electrical Circuits

The power (P) dissipated by a resistor in an electrical circuit can be calculated using the formula P = IV, where I is the current through the resistor and V is the voltage across it. Additionally, using Ohm's Law, power can also be expressed as P = I²R or P = V²/R, allowing for flexibility in calculations depending on the known quantities.

Resistor Power Rating

The power rating of a resistor indicates the maximum amount of power it can safely dissipate without overheating. Exceeding this rating can lead to increased temperature, potentially damaging the resistor. It is crucial to select a resistor with an appropriate power rating for the application to ensure reliability and safety in electrical circuits.