Question: Suppose you manage a factory that uses many electric motors. The motors create a large inductive load to the electric power line, as well as

Suppose you manage a factory that uses many electric motors. The motors create a large inductive load to the electric power line, as well as a resistive load. The electric company builds an extra-heavy line to supply you with a component of current that is 90° out of phase with the voltage, as well as with current in phase with the voltage. The electric company charges you an extra fee for “reactive volt-amps,” in addition to the amount you pay for the energy you use. You can avoid the extra fee by installing a capacitor between the power line and your factory. The following problem models this solution. In an RL circuit, a 120-V (rms), 60.0-Hz source is in series with a 25.0-mH inductor and a 20.0-P resistor. What are (a) The rms current and
(b) The power factor?
(c) What capacitor must be added in series to make the power factor 1?
(d) To what value can the supply voltage be reduced, if the power supplied is to be the same as before the capacitor was installed?

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