Top Circuit is resistance coil (coil plus resistor) to power 50 volt 10 amp Carbon Arc Health Lamp. Power calculation is:
110 volts times 10 amps = 1100 watts.
Bottom Circuit is AC Choke Coil or wire wrapped around the leg of laminated iron core. This looses 50 watts in this circuit. Power Calculation is:
Carbon Arc Health Lamp at 500 watts
Looses of AC Choke Coil 50 watts
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Total Looses 550 watts
Difference between top minus bottom circuit
1100 watts
550 watts
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550 watts
In simulator bottom circuit, I lowered power line voltage and resistance to show math changes in circuit.
AC Choke Coil Design has to match voltage requirements of device powered, frequency, current, and wire size in choke coil.