Question

An air conditioner connected to a 120 V rms ac line is equivalent to an 11.0-ohm resistance and a 1.59-ohm inductive reactance in series. (a) Calculate the impedance of the air conditioner. (b) Calculate the average rate at which energy is supplied to the appliance.

Answer 1

(a). The impedance of the air conditioner is 11.11 ohm.

(b). The average rate of energy delivery is
`1.28*10^(3)\ W`

Step-by-step explanation:

Given that,

Voltage = 120 V

Resistance = 11.0 ohm

Inductive reactance = 1.59 ohm

(a). We need to calculate the impedance of the air conditioner

Using formula of impedance

`Z=\sqrt{R^2+X_(L)^2}`

Put the value into the formula

`Z=√(11.0^2+1.59^2)`

`Z=11.11\ Omega`

(b). We need to calculate the average rate of energy delivery

Using formula of power

`P_(avg)=I^2* R`

Where, I=Current

R = resistance

`P_(avg)=((V_(rms))/(Z))^2R`

Put the value into the formula

`P_(avg)=((120)/(11.11))^2*11.0`

`P_(avg)=1283.29\ W`

`P_(avg)=1.28*10^(3)\ W`

Hence, (a). The impedance of the air conditioner is 11.11 ohm.

(b). The average rate of energy delivery is
`1.28*10^(3)\ W`