Question

A 4.0 -k \(W\) heater is designed to be connected to a \(120-V\) ms source. What is the power dissipated by the heater if it is instead connected to a \(120-\mathrm{V}\) de source?

Short answer

Answer: The power dissipated by the heater when connected to a 120 V DC source is 4000 W, or 4 kW.

Step-by-step solution

Calculate the resistance of the heater

To find the resistance of the heater, we can use the formula for power in terms of voltage and resistance: \(P = \frac{V^2}{R}\). Rearrange this formula for resistance, \(R = \frac{V^2}{P}\). We know the power provided by the heater is 4 kW, or 4000 W, and the RMS voltage is 120 V. So we have: \(R = \frac{(120 V)^2}{4000 W}\) Calculating the resistance: \(R = \frac{14400 V^2}{4000 W} = 3.6 \,\Omega\)

Calculate the power dissipated by the heater using DC source

Now we have the resistance of the heater, and we are given a 120 V DC source. We can calculate the power dissipated by the heater using the same power formula, \(P = \frac{V^2}{R}\). Plug in the DC voltage of 120 V and the resistance of 3.6 Ohms: \(P = \frac{(120 V)^2}{3.6 \,\Omega}\) Calculating the power: \(P = \frac{14400 V^2}{3.6 \,\Omega} = 4000 W\) Thus, the power dissipated by the heater when connected to a 120 V DC source is 4000 W, or 4 kW.