THE UNIVERSITY OF BRITISH COLUMBIA
 
Physics 108 Assignment # 9:
 
INDUCTANCE & CIRCUITS
 
Wed. 9 Mar. 2005 - finish by Wed. 16 Mar.

1. Solenoid as an $RL$ Circuit: A long wire with net resistance $R = 120$ $\Omega$ is wound onto a nonmagnetic spindle to make a solenoid whose cross-sectional area is $A = 0.02$ m$^2$ and whose effective length is $\ell = 0.5$ m. (Treat the coil as an ideal, long solenoid.) Using a battery with a 1 M$\Omega$ internal resistance, a magnetic field of $B_0 = 0.6$ T has been built up inside the solenoid. At $t=0$ the battery is shorted out and then disconnected so that the current begins to be dissipated by the coil's resistance $R$. We find that after 3.6 ms the field in the coil has fallen to 0.1 T.
   1. How many joules of energy are stored in the coil at $t=0$?
   2. How long does it take for the stored energy to fall to half its initial value?
   3. What is the total number of turns in the coil?

2. $LC$ Circuit Time-Dependence: In an $LC$ circuit with $C = 90$ $\mu$F the current is given as a function of time by $I = 3.4\cos ( 1800t + 1.25)$, where $t$ is in seconds and $I$ is in amperes.
   1. How soon after $t=0$ will the current reach its maximum value?
   2. Calculate the inductance.
   3. Find the total energy in the circuit.

3. Build Your Own Circuit: You are given a 12 mH inductor and two capacitors of 7.0 and 3.0 $\mu$F capacitance. List all the resonant frequencies that can be produced by connecting these circuit elements in various combinations.

4. $LRR$ Circuit Time-Dependence: In the circuit shown, the ${\cal E} = 12$ V battery has negligible internal resistance, the inductance of the coil is $L = 0.12$ H and the resistances are $R_1 = 120$ $\Omega$ and $R_2 = 70$ $\Omega$. The switch S is closed for several seconds, then opened. Make a quantitatively labelled graph with an abscissa of time (in milliseconds) showing the potential of point A with respect to ground, just before and then for 10 ms after the opening of the switch. Show also the variation of the potential at point B over the same time period.