THE UNIVERSITY OF BRITISH COLUMBIA
 
Physics 108 Assignment # 10:
 
AC CIRCUITS & EM WAVES
 
Wed. 16 Mar. 2005 - finish by Wed. 23 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}

    1. What maximum inductance $L$ is required if the power in the light bulb is to be varied by a factor of five?
    2. 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.
    1. Write expressions for all three components of the magnetic field associated with the wave.
    2. Find the wavelength of the wave.


Jess H. Brewer
2005-03-13