A 64.0-ohm resistor is connected in series with a 40.0-mu F capacitor and a gene
ID: 1325192 • Letter: A
Question
A 64.0-ohm resistor is connected in series with a 40.0-mu F capacitor and a generator having a maximum voltage of 1.20 x 10^2 V and operating at 60.0 Hz. (a) Find the capacitive reactance of the circuit. ohm (b) Find the impedance of the circuit. ohm (c) Find the maximum current in the circuit. A (d) Does the voltage lead or lag the current? The voltage leads the current. The voltage lags the current. (e) How will putting an inductor in series with the existing capacitor and resistor affect the current? Explain.Explanation / Answer
R=64 ohm
C=40uF
V=120V
f=60hz
a)Capacitance reactance=
XC=1/(2*PIE*FC)
XC=1/(2*3.14*60*40*10^-6)
1/15072*10^-6
=6.6e-5e6
=66
b)impedance of circuit
Z=R+jwL
w=2*3.14*60
=376.8 radian
Impedance=376.8j
Z=underroot(R^2+X^2)
=underoot(64^2+376.8^2)
=382.19ohm
c)total currentI=120/382.19
=0.313 Amp
d)In series, the current is the same in both L and R. The voltage in R will be in phase with the current in R, but the voltage across L will lead the current through L.
e)Reactive power does not register on your wathour meter. You don't pay for it. But it adds to the total KVA of the power company;s system. As such, power is wasted in the transmission lines. It doesn't ride free.
The power company is penalized by low power factors because they have to furnish the equipment and fuel to supply the KVAR component of their power lines. You, as a customer of the power company, pay for this wasted energy as the power company passes the cost on to you.
The resistance is not changed when capacitors are added to the circuit. Resistance applies to the KW portion of the power triangle. The reactance of inductors and capacitors are 180 degrees out of phase. When capacitors are installed, the total impedance of the circuit is reduced, as well as the KVA of the circuit. The capacitor stores energy in one half of the cycle and releases it during the next half cycle. This energy circulates around the circuit supplying the inductance for motor and other inductive equipment.
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