In a power system, the voltage and currents for a Y-connected load are given asV(t)=220cos(ωt-20°)I(t)=110sin(ωt +30°)What is the load impedance in each phase?
Question
In a power system, the voltage and currents for a Y-connected load are given asV(t)=220cos(ωt-20°)I(t)=110sin(ωt +30°)What is the load impedance in each phase?
Solution
To find the load impedance in each phase, we need to use Ohm's law, which states that the impedance (Z) is equal to the voltage (V) divided by the current (I).
Given that the voltage V(t) = 220cos(ωt-20°) and the current I(t) = 110sin(ωt +30°), we can find the magnitude and phase angle of each.
The magnitude of the voltage is 220V and the phase angle is -20°. The magnitude of the current is 110A and the phase angle is +30°.
The phase difference between the voltage and the current is -20° - (+30°) = -50°.
So, the impedance Z = V/I = 220/110 = 2 Ω.
The phase of the impedance is the phase of the voltage minus the phase of the current, which is -50°.
Therefore, the load impedance in each phase is 2∠-50° Ω.
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