Physics, Circuits Containing Resistance, Capacitance, and Inductance?

A light bulb has a resistance of 230 . It is connected to a standard wall socket (120 V rms, 60.0 Hz).





(a) Determine the rms current in the bulb.





(b) Determine the rms current in the bulb after a 13.0 µF capacitor is added in series in the circuit.





(c) It is possible to return the current in the bulb to the value calculated in part (a) by adding an inductor in series with the bulb and the capacitor. What is the value of the inductance of this inductor?

Physics, Circuits Containing Resistance, Capacitance, and Inductance?
Resistance changes with temperature.


(a) Provided that the stated resistance is that of the hot bulb, the rms current will be 120 Volts/230 Ohms = 0.5217 Amps.


(b) Next let's calculate the Impedance of the Capacitor at 60 Hz : Xc=1/(2*Pi*f*C) (notice that Xc=1/2PifC): = 1/[6.2832*(60 Hz)*(13*10^-6)] = ~204 Ohms.


230 in series with 204 = 434 Ohms


120 Volts/434Ohms = 0.276 Amps


(c) To counteract the presence of the capacitor we will connect an inductor in series. It's impedance would have to be the same as that of the capacitor: Xl=2*Pi*f*L (notice that Xl=2PifL), Xl=204, let's calculate L:


L=Xl/(2*Pi*f) = 204/(6.2832*60) = 0.54113 Henries


I hope I didn't make a mistake in the calculations.