Week 9: Alternating Current Circuits 337
high frequency pulses while maintaining a steadyDCvoltage across the fully charged capacitor. In
this configuration, the capacitor can also serve as a reservoir of charge and can maintain the voltage
even if the load imposes a transient peak in demand that is higher thanthe supply voltage source
could otherwise handle.
Problem 4.
VL VRLRepeat the previous problem for theLRcircuit above, evaluatingI(t),δ,VR(t),VL(t) in terms
of the dimensionlessωLR. This circuit is used as alow pass filter, with peak current through and
voltage acrossRatlowfrequencies, while high frequencies are blocked by the inductor.
When might one wish to use theVLversus theVRvoltage taps, respectively? Think about this:
Not all loads areresistive...
Problem 5.
CLRAseriesLRC circuit connected across a variable AC voltage sourceV =V 0 cos(ωt) is drawn
above. Find:
a) The currentI(t) in the primary supply wire (as shown in the figure above) with all terms, e.g.
the phaseδ, and the impedanceZdefined (the latter in terms of the individual reactances).
b) Theaveragepower dissipated by the circuit. Remember,P(t) =V(t)I(t) (whereV(t) is the
voltage across each circuit element andI(t) is the common current through it). Two of the circuit
elements havezeroaverage power, but you must prove this.
Hint: To find the answer you must assume that:I(t) =I 0 cos(ωt−δ)and then add thevoltage dropacross each series element. Your answer for Z should remind you of
series addition of resistors, using reactances instead (two of which areπ/2 out of phase with the
resistor).
Problem 6.