Question$4[12$ marks$]$

I. $[4]$ An industrial heater has a nameplate that reads: $210$ V $60$ Hz $12$ kVA $0\mathrm{.}78$ pf lagging Determine:

a$.$the apparent and the complex power

b$.$the impedance of the heater

c$.$Find the value of the capacitance C that must be connected across the heater to raise the pf to unity.

II$.[4]$ A transmitter delivers maximum power to an antenna when the antenna is adjusted to represent a load of $75-$ resistance in series with an inductance of $4H.$ If the transmitter operates at $4\mathrm{.}12$ MHz $,$ find its internal impedance.

III. $[4]$ For each vertical set of two measurements appearing in Fig. $4-$III, determine the Th$$venin equivalent circuit.

Fig $4-$III

$($a$)$

$($b$)$