Answer:
The impedance Z₁ is [tex]10+j6.19\ kVA[/tex]
Explanation:
Given that,
Dissipates power = 10 kW
Power factor = 0.85
Apparent power = 0.75
Frequency = 60 Hz
Suppose we need to calculate the impedance Z₁
The impedance Z₁ dissipates 10 kW with a power factor of 0.85 lagging
[tex]\cos\theta=0.85[/tex]
[tex]\theta=\cos^{-1}(0.85)[/tex]
[tex]\theta=31.78^{\circ}[/tex]
We need to calculate the impedance Z₁
Using formula of the impedance Z₁
[tex]z_{1}=P_{1}+jQ_{1}[/tex]
[tex]z_{1}=P_{1}+j\dfrac{10}{0.85}\sin\theta[/tex]
Put the value into the formula
[tex]z_{1}=10+j\dfrac{10}{0.85}\sin31.78[/tex]
[tex]z_{1}=10+j6.19\ kVA[/tex]
Hence, The impedance Z₁ is [tex]10+j6.19\ kVA[/tex]
