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. If the power rating of a 15 kΩ resistor is 5.0 W, what is the maximum allowable potential difference across the terminals of the resistor?

Verified step by step guidance

1. Understand the relationship between power, voltage, and resistance. The formula for power dissipated by a resistor is given by: $P=\frac{V^2}{R}$, where $P$ is the power, $V$ is the voltage, and $R$ is the resistance.
2. Identify the given values: The power rating $P$ is 5.0 W and the resistance $R$ is 15 kΩ (which is 15,000 Ω).
3. Rearrange the formula to solve for the voltage $V$: $V=\sqrt{P\times R}$.
4. Substitute the known values into the rearranged formula: $V=\sqrt{5.0\times 15000}$.
5. Calculate the square root to find the maximum allowable potential difference $V$ across the terminals of the resistor.

Key Concepts

Power Rating

The power rating of a resistor indicates the maximum power it can dissipate safely without overheating. It is crucial for preventing damage due to excessive heat, which can alter the resistor's properties or cause it to fail. The power rating is typically specified in watts (W) and helps in selecting the appropriate resistor for a given application.

Ohm's Law

Ohm's Law is a fundamental principle in electronics that relates voltage (V), current (I), and resistance (R) in a circuit: V = I * R. This law is essential for calculating the potential difference across a resistor when the current and resistance are known, or vice versa. It provides a basis for understanding how electrical components interact in a circuit.

Power Dissipation in Resistors

Power dissipation in resistors is calculated using the formula P = V^2 / R, where P is the power, V is the voltage across the resistor, and R is the resistance. This concept is vital for determining how much power a resistor can handle without exceeding its power rating, ensuring safe operation within electrical circuits.