Question

An air conditioner connected to a 120 V rms ac line is equivalent to a 9.66 O resistance and a 1.43 O inductive reactance in series. Calculate (a) the impedance of the air conditioner and (b) the average rate at which energy is supplied to the appliance.

Answer 1

The impedance (Z) is the combined resistance and inductive reactance for an AC circuit and can be used to calculate the average rate of energy supplied to an appliance such as an air conditioner.

Step-by-step explanation:

The air conditioner connected to a 120 V rms AC line, with a resistance (R) of 9.66 ohms and an inductive reactance (XL) of 1.43 ohms forms a series RLC circuit without a capacitor. (a) The impedance (Z) of the air conditioner is calculated using the formula Z = √(R2 + XL2), which yields Z = √(9.662 + 1.432). (b) The average rate of energy supplied, also known as the average power (P), is found using the formula P = Vrms2 / Z, where Vrms is the root mean square voltage and Z is the impedance.