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A balanced three-phase source serves the following loads: Load $1: 20 \mathrm{kVA}$ at $0.8 \mathrm{pf}$ lagging Load $2: 10 \mathrm{kVA}$ at $0.7 \mathrm{pf}$ lead...

Question

A balanced three-phase source serves the following loads: Load $1: 20 \mathrm{kVA}$ at $0.8 \mathrm{pf}$ lagging Load $2: 10 \mathrm{kVA}$ at $0.7 \mathrm{pf}$ leading Load $3: 10 \mathrm{kW}$ at unity pf Load $4: 16 \mathrm{kVA}$ at $0.6 \mathrm{pf}$ lagging The line voltage at the load is $208 \mathrm{V}$ rms at $60 \mathrm{Hz}$, and the line impedance is $0.02+j 0.04 \Omega$. Find the line voltage and power factor at the source.

A balanced three-phase source serves the following loads: Load $1: 20 \mathrm{kVA}$ at $0.8 \mathrm{pf}$ lagging Load $2: 10 \mathrm{kVA}$ at $0.7 \mathrm{pf}$ leading Load $3: 10 \mathrm{kW}$ at unity pf Load $4: 16 \mathrm{kVA}$ at $0.6 \mathrm{pf}$ lagging The line voltage at the load is $208 \mathrm{V}$ rms at $60 \mathrm{Hz}$, and the line impedance is $0.02+j 0.04 \Omega$. Find the line voltage and power factor at the source.



Answers

In an $L-R-C$ series circuit the magnitude of the phase angle is 54.0$^\circ$, with the source voltage lagging the current. The reactance of the capacitor is 350 $\Omega$, and the resistor resistance is 180 $\Omega$. The average power delivered by the source is 140 W. Find (a) the reactance of the inductor; (b) the rms current; (c) the rms voltage of the source.


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