Question

n air conditioner connected to a 120 V rms ac line is equivalent to a 16.3 Ω resistance and a 1.29 Ω 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

16.35175 Ω

646.27188 W

Step-by-step explanation:

R = Resitance = 16.3 Ω

`X_L` = Inductive resistance = 1.29 Ω

`V_r` = RMS voltage = 120 V

The impedance of an LC circuit is given by

`Z=√(R^2+X_L^2)\\\Rightarrow Z=√(16.3^2+1.3^2)\\\Rightarrow X=16.35175\ \Omega`

The impedance of the air conditioner is 16.35175 Ω

The average rate of energy is given by

`P_a=I_r^2R\\\Rightarrow P_a=\left((V_r)/(Z)\right)^2R\\\Rightarrow P_a=\left((120)/(16.35175)\right)^2* 12\\\Rightarrow P_a=646.27188\ W`

The average rate at which energy is supplied to the appliance is 646.27188 W