The power dissipated by a resistor can be calculated using the formula \(P = \frac{V^2}{R}\), where \(P\) is the power in watts, \(V\) is the potential difference in volts, and \(R\) is the resistance in ohms. We are given that the resistor generates 200 J of heat every second, which means its power is 200 W (since 1 watt = 1 joule/second). The resistance is 8 Ω.
We can rearrange the formula to solve for \(V\):
\(V = \sqrt{PR}\)
Substituting the given values:
\(V = \sqrt{200 \, W \times 8 \, \Omega} = \sqrt{1600 \, W\Omega} = 40 \, V\)
Therefore, the potential difference across the resistor is 40 V.
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