What is the peak current through a 400–W room heater that operates on 120–V AC power?
To find the peak current through the room heater, we can use Ohm's Law and the formula for power.
First, let's calculate the resistance of the room heater. We know that power (P) is equal to the voltage (V) squared divided by the resistance (R), so we can rearrange the formula to solve for resistance:
R = V^2 / P
Given that the power of the room heater is 400 watts (W) and the voltage is 120 volts (V), we can plug these values into the formula:
R = 120^2 / 400
R = 36,000 / 400
R = 90 ohms
Now that we have the resistance, we can use Ohm's Law to find the current (I). Ohm's Law states that current is equal to the voltage (V) divided by the resistance (R):
I = V / R
Substituting the voltage and resistance values:
I = 120 / 90
I ≈ 1.33 Amperes
Therefore, the peak current through the room heater is approximately 1.33 Amperes.
power = i V
400 = i (120)
i = 3.33 rms
i peak = i rms * sqrt 2 = 4.71 amps peak