Answer:
(a). The impedance of the air conditioner is 11.11 ohm.
(b). The average rate of energy delivery is [tex]1.28\times10^{3}\ W[/tex]
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
[tex]Z=\sqrt{R^2+X_{L}^2}[/tex]
Put the value into the formula
[tex]Z=\sqrt{11.0^2+1.59^2}[/tex]
[tex]Z=11.11\ Omega[/tex]
(b). We need to calculate the average rate of energy delivery
Using formula of power
[tex]P_{avg}=I^2\times R[/tex]
Where, I=Current
R = resistance
[tex]P_{avg}=(\dfrac{V_{rms}}{Z})^2R[/tex]
Put the value into the formula
[tex]P_{avg}=(\dfrac{120}{11.11})^2\times11.0[/tex]
[tex]P_{avg}=1283.29\ W[/tex]
[tex]P_{avg}=1.28\times10^{3}\ W[/tex]
Hence, (a). The impedance of the air conditioner is 11.11 ohm.
(b). The average rate of energy delivery is [tex]1.28\times10^{3}\ W[/tex]
