A 1-W, 350-12 resistor is connected to 24 V. Is this resistor operating within its power rating?
The correct answer and explanation is :
To determine whether the 1-Watt, 350-ohm resistor is operating within its power rating when connected to a 24-volt source, we need to calculate the actual power it dissipates and compare it with its rated power.
Step 1: Use Ohm’s Law to Find the Power
We can calculate the power dissipated using the formula:
$$
P = \frac{V^2}{R}
$$
Where:
- $P$ is the power in watts,
- $V$ is the voltage (24 V),
- $R$ is the resistance (350 ohms).
$$
P = \frac{24^2}{350} = \frac{576}{350} \approx 1.646 \text{ W}
$$
Step 2: Compare with Power Rating
- Calculated Power: ≈ 1.65 W
- Rated Power: 1 W
Since 1.65 W > 1 W, the resistor exceeds its power rating.
Conclusion:
No, the resistor is not operating within its power rating. It dissipates more power than it’s rated for, which can lead to overheating, damage, or failure.
Explanation (300 words):
Electrical resistors are rated for a maximum amount of power they can safely dissipate as heat without being damaged. This rating, given in watts (W), ensures the resistor can operate safely under specified voltage and current conditions. In this scenario, we are given a 350-ohm resistor rated for 1 watt, connected across a 24-volt source.
To determine if this resistor is operating safely, we apply the power formula: $P = V^2 / R$. Squaring the 24 volts gives 576, which divided by 350 ohms results in about 1.65 watts. This value is clearly higher than the resistor’s rated limit of 1 watt.
When a resistor exceeds its power rating, it can overheat. Heat builds up faster than it can be dissipated, potentially causing the resistor’s material to break down, changing its resistance or leading to an open circuit. In extreme cases, it can even result in fire or damage to nearby components.
To safely use a resistor in a circuit, engineers generally design with a safety margin—often selecting a resistor rated for at least twice the expected power dissipation. In this case, a resistor rated at 2 watts or more would be more appropriate.
Therefore, connecting a 1-watt, 350-ohm resistor directly to a 24V source is unsafe and should be avoided.