# Homework Assignment #6

Due: Tuesday 14 July 1998

Chapters 33 and 34.

### QUESTIONS

Chapter 33 - 1, 3, 5, 8, 12, 17, 19, 20, 22, 23, 28.
Chapter 34 - 1, 12, 13, 14, 19.

### PROBLEMS

Chapter 33 - 8, 12, 18, 19A, 19, 24, 25, 29, 31, 37, 45, 59, Review Problem.
Chapter 34 - 1, 2, 6, 12, 19, 25.

These are the ANSWERS only, not the SOLUTIONS. It is not sufficient to copy these and turn them in as homework. You must show your work.

Q 33-1) The voltage across the inductor peaks first, then one quarter of a cycle later the current through the inductor reaches its maximum value.

Q 33-3) The reactance of a capacitor 1/(wC) is frequency dependent. At high frequencies (large w) the capacitive reactance is small and the cap offers no impedance to current flow, behaving like a short (a piece of wire). At low frequencies (small w) the capacitive reactance is large and the cap offers much impedance to current flow behaving like an open (a break in the wire).
Q 33-5) The voltages across the resistor, capacitor, and inductor do not all peak at the same time. Kirchhoff's voltage law, which is just energy conservation, is satisfied at ANY ONE TIME.
Q 33-8) R is not frequency dependent;
XL doubles;
XC is halved.
Q 33-12) At resonance, Z (the impedance) equals R (the resistance).
Q 33-17) No, transformers are strictly AC devices. The changing current in one coil causes a changing magnetic field, which causes a changing magnetic flux in another coil, which induces an emf by Faraday's law (Lenz' law) in the second coil, which pushes a current in the second coil.
Q 33-19) The time average is zero; the graph spends as much time above zero level as below. The root-mean-square voltage is Vmax/sqrt(2).
Q 33-20) The time average is Vmax/2. The root-mean-square voltage is Vmax/sqrt(2).
Q 33-22) No. If the RLC circuit is capacitive, the current leads the applied voltage; if the RLC circuit is inductive, the current lags the applied voltage.
Q 33-23) No, power is only dissipated in resistors.
Q 33-28) The iron has a high permeability and concentrates the lines of magnetic field to the inside of the coils, instead of letting B lines spread all over space. They are only useful to the transformer if the B lines pass through the coils.
Q 34-1) The momentum given to the reflecting surface by light photons is twice as large as the momentum given to the absorbing surface. The radiation pressure is the sum of all the microscopic momentum transfers. The same effect would be seen if bullets were fired at two walls, one reflecting the bullets and one absorbing the bullets.
Q 34-12) Oscillating electric fields push electrons in the metal antenna up and down, creating a current.
Q 34-13) A changing magnetic flux through the conducting loop antenna induces a current around the loop.
Q 34-14) The voltage induced in a VHF dipole antenna by the electric field in the signal is V = Ed.
The voltage (emf) induced in a UHF loop antenna by the magnetic field in the signal is V = -d/dt(magnetic flux) = (Area of loop) (cos theta) dB/dt. Because the oscillating magnetic field is B(t)=B0sin(kx-wt), the derivative dB/dt will be proportional to the angular frequency of oscillation (w).
Q 34-19) There is no signal directly over (or under) a dipole antenna.
P 33-8) 0.413 Wb
P 33-12) 3.14 A
P 33-18)
1. 141 A
2. 235 A

P 33-19A) C Vmax
P 33-19) 2.77 nC
P 33-24) 2792 Hz
P 33-25)
1. 78.5 ohms
2. 1590 ohms
3. 1520 ohms
4. 0.138 A
5. -84.3 degrees

P 33-29) 1.88 V
P 33-31)
1. 146 V
2. 213 V
3. 179 V
4. 33.3 V

P 33-37) 8 W
P 33-45) 1.82 pF
P 33-59) 687 V
P 33-Review Problem)
1. Vmax/R sin(wt)
2. Vmax2/2R
3. Vmax/sqrt[R2 + (wL)2] cos[wt + arctan(wL/R)]
4. 1/(w2L) at the resonant frequency W
5. Z=R at the resonant frequency W
6. Vmax2L/2R2
7. (same as above)
8. arctan[3/2R sqrt(L/C)]
9. w/sqrt(2)

P 34-1) 680 years from now
P 34-2) 7.33 x 10-7 T
P 34-6) 3c/4 = 2.25 x 108 m/s
P 34-12) 3.33 x 10-6 J/m3
P 34-19)
1. 3.32 x 105 W/m2
2. Esurface = 1880 V/m
Bsurface = 2.22 x 10-4 T

P 34-25) 8.33 x 10-8 Pa (1 Pa = 1 N/m2)

Please report any corrections to Professor Scalise.