A 450??(ohms) resistor and a 6.50? u F capacitor are connected in parallel to an

Question

A 450??(ohms) resistor and a 6.50?uF capacitor are connected in parallel to an ac generator that supplies an rms voltage of 220V at an angular frequency of 360 rad/s . Note that since there is no inductor in the circuit, the 1/?L term is not present in the expression for Z.

Part A

Find the current amplitude in the resistor.

Part B

Find the current amplitude in the capacitor.

Part C

Find the phase angle of the source current with respect to the source voltage.

Part D

Find the amplitude of the current through the generator.

Part E

Does the source current lag or lead the source voltage?

Explanation / Answer

AC and "constant voltage amplitude" don't go together. I'll assume the 220V is RMS voltage.
? = 360,

w=2*3.14*f

360/6.28=f

f=57.32 Hz

Capacitive Reactance Xc = 1/(2?fC) = 1/2*3.14*57.32*6.50*10^-6

=0.000427*10^6

=427ohm

Next unknown is the connection between the R and C? I'll assume they are in parallel and connected across the generator.

a)Current through the resistor is 220/450 = 0.488amps RMS
b)Current through the cap is 220/427 = 0.515 amps RMS
c)Phase angle ? = arctan (X/R)

=arctan(427/450)

=43.48 degrees

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