Final answer:
The power dissipated in the inductor is 7152 watts.
Step-by-step explanation:
To find the power dissipated in an inductor, we can use the formula P = IV, where P is power, I is current, and V is voltage. In this case, the voltage supplied to the inductor is 400V. To find the current, we need to calculate the impedance of the inductor, which is given as Z = 20 + j10. Since the impedance is a complex number, we can find the magnitude of the impedance using the formula Z = sqrt(R^2 + X^2), where R is the resistive part and X is the reactive part. In this case, R = 20 and X = 10. Substituting these values into the formula, we get Z = sqrt((20^2) + (10^2)) = sqrt(400 + 100) = sqrt(500) = 22.36. Now we can find the current by dividing the voltage by the impedance: I = V/Z = 400/22.36 = 17.88A. Finally, we can find the power dissipated by multiplying the current by the voltage: P = IV = 17.88 * 400 = 7152 watts.