Notes for July 9, 2008
Prepared by: Katie Daniel
Conceptual Problems
1. (Erica Andrist borrowed from 2007 Practice Exam, #13)
In an RLC series circuit, if the AC frequency is increased to a very large value, what value does the phase angle
(the lag in the phase of the current with respect to the voltage) between the current and voltage approach?
a. 90°
b. 0°
c. -90°
d. 45°
e. -45°
The answer is a. 90°
The sum of the three vectors VL, VC, and VR results in Vtotal. Current is always with VR.
Using phase diagrams gives a better qualitative understanding.
VL = IXL
XL=2πfL
VC = IXC
XC=1 / 2πfL
If VL is much greater than VC, VL keeps increasing and you eventually get 90° (as in the diagram above).
2. (Erica Andrist borrowed from “AC Circuits” at http://www.allaboutcircuits.com/vol_2/index.html)
When is the instantaneous voltage in an inductor at its maximum? At zero? How about the current?
VL = iXL
Answer: It is at its maximum when I is 0, and is 0 when I is at its maximum.
ε = -LΔi/Δt
3. (Lisa Albrecht borrowed it from the text, page 572, #11)
If the resistance in an RLC circuit remains the same, but the capacitance and inductance are each doubled, how
will the resonance frequency chance?
Using the equation ωres = 1/ √LC we can see that doubling L and C will result in halving ωres.
4. (Lisa Albrecht borrowed from the textbook, page 557, Checkpoint 21.3)
True of False: The average power delivered by a generator in a series RLC circuit has its maximum value when
the inductive reactance equals the capacitive reactance.
True, because V = IZ, so Vrms = IrmsZ
Pavg = Irms2R
So Z = √R2 + (XL-XC)2
(Extra conceptual problems by mistake)
5. (Monique Pogreba borrowed it from the text, page 572, #12)
Why is the sum of the max voltage across each of the elements in a series RLS circuit usually greater than the
max applied voltage? Does this violate Kirchoff Rule? Explain.
You can’t just add L, C, and R because they maximize at different times (they are out of phase).
Vmax = √VRmax2 + (VLmax-VCmax)2
But Vmax ≠ VRmax + VLmax + VCmax (as you would do with a DC cylinder)
6. (Monique Pogreba borrowed it from the text, page 572, #8)
How can the average value of an alternating current be zero, yet the square root of the average squared value
not be zero?
Iavg = 0
√(Iavg)2 ≠ 0, because this will always give a number greater than or equal to zero (a positive quantity).