What power is consumed by a 10 kW heat strip rated 230V when connected to a 115V circuit?

To determine the power consumed by the heat strip rated at 10 kW when connected to a lower voltage circuit of 115V, it's important to first understand how power is affected by changes in voltage and resistance.

The heat strip's original power rating of 10 kW at 230V implies a specific resistance based on the relationship between power, voltage, and resistance, given by the formula:

[ P = \frac{V^2}{R} ]

From this formula, we can rearrange it to solve for resistance:

[ R = \frac{V^2}{P} = \frac{(230V)^2}{10,000W} = 5.29 , \Omega ]

When the heat strip is connected to a 115V circuit, we can find the new power consumption by substituting the lower voltage into the power formula again:

[ P_{new} = \frac{V^2}{R} = \frac{(115V)^2}{5.29 , \Omega} ]

Calculating this gives:

[ P_{new} = \frac{13225}{5.29} \approx 2,500W \text{ or } 2.50