# Question Video: Determining the Maximum Safe Voltage for a Resistor

What is the maximum voltage that can be safely applied to a 15 kΩ resistor that has a 10 W power rating?

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### Video Transcript

What is the maximum voltage that can be safely applied to a 15-kiloohm resistor that has a 10-watt power rating?

The idea behind a power rating is it’s the maximum power that can safely be transmitted through a given circuit element, in this case, a resistor. We could write then that 𝑃 sub max, the maximum power through the resistor, is equal to 10 watts. To solve for the maximum voltage that can be safely applied to this resistor, we’ll want to find the relationship that connects voltage, resistance, and power.

A relationship that does just this says that power in an electrical circuit is equal to the potential squared divided by the resistance. In our case, we can write that the maximum power is equal to the maximum voltage squared divided by resistance. And then, rearranging this equation to solve for 𝑉 sub max, we find it’s equal to the square root of 𝑃 sub max, the maximum power, times the resistor’s resistance.

We’ve seen that maximum power is 10 watts. And, in addition, the resistance value of our resistor 𝑅 is equal to 15 kiloohms or 15000 ohms. Using these units, we plug in these values and then solve for 𝑉 sub max. To two significant figures, it’s 390 volts. That’s the maximum voltage that can be safely applied to this resistor.