THE UNIVERSITY OF BRITISH COLUMBIA
 
Physics 122 Assignment # 10:
 
AC CIRCUITS & EM WAVES
 
Fri. 15 Mar. 2002 - finish by Fri. 22 Mar.

1.
A typical ``light dimmer" switch consists of a variable inductor L connected in series with the light bulb B as shown in the diagram on the right. The power supply produces 120 V (rms) at 60.0 Hz and the light bulb is marked ``120 V, 1000 W." Assume that the light bulb is a simple resistor whose resistance does not depend on its temperature.

\begin{figure}\begin{center}\mbox{ \epsfysize 1.5in \epsfbox{PS/dimmer.ps} } \end{center} \end{figure}

(a)
What maximum inductance L is required if the power in the light bulb is to be varied by a factor of five?
(b)
Could one use a variable resistor in place of the variable inductor? If so, what maximum resistance R would be required? Why isn't this done? (Variable resistors [rheostats] are generally cheaper than variable inductors.)

 

2.
LCR CIRCUIT TIME-DEPENDENCE:   In the circuit shown, the battery has negligible internal resistance. The switch S is closed for a long time, then opened. Describe qualitatively what happens in the circuit after the switch is closed and then after it is opened again, for two cases:
(a)   $R/2L > 1/\sqrt{LC}$   and
(b)   $R/2L < 1/\sqrt{LC}$.

\begin{figure}\begin{center}\mbox{ \epsfysize 1.4in \epsfbox{PS/lcr.ps} } \end{center} \end{figure}

 

3.
ELECTROMAGNETIC WAVE:   The electric field associated with a plane electromagnetic wave is given by

\begin{displaymath}E_x = 0, \quad E_y = 0 \quad \hbox{\rm and} \quad E_z = E_0 \sin[k(x - ct)] , \end{displaymath}

where $E_0 = 2.34 \times 10^{-4} $ V/m and $k = 9.72 \times 10^6 $ m-1. The wave is propagating in the +x direction.
(a)
Write expressions for all three components of the magnetic field associated with the wave.
(b)
Find the wavelength of the wave.


Jess H. Brewer
2002-03-14