Physics 2910G Homework Assignment 1, 2012

Physics 2910G Homework Assignment 1, 2012
1. Consider the circuit below.
Due date Wednesday February 1.
(a) find the potential difference V ab between points A and B.
(b) imagine connecting a wire of zero resistance between A and B. Find the current i
flowing in that wire.
2. In the circuit below, find the current in resistor R 2 .
3. In the circuit shown below, the current through the 220 ohm resistor is 0.10
amperes.
(a) calculate the power dissipated by the 47 ohm resistor.
(b) calculate the EMF of the battery.

4. Consider the circuit below, in which an AC voltage source is connected to a
combination of a resistor, a capacitor and an inductor.
(a) write an expression for the (complex) impedance of the circuit.
(b) find the magnitude of the impedance, in form A+jB
(c) find an expression for the frequency at which the impedance is a maximum or
minimum. Indicate whether it is a maximum or a minimum.
(d) find expressions for the limiting behaviour of the impedance at very low and very
high frequencies.
5. In the circuit show below, C1 = 5 microfarads, C2 = 10 microfarads and R =
1000 ohms. Initially, the switch is open, C1 is charged to 20 volts, and C2 is uncharged.
At time t=0 the switch is closed.
(a) Calculate the voltage across C1 at a much later time. Hint: consider charge
conservation.
(b) The energy stored in a charged capacitor is given by U = CV 2 /2. Calculate the energy
stored in C1 and C2 before and after closing the switch.
(c) Derive an expression for the power dissipated in R as a function of time for t>0.
(d) Integrate your expression from (c) to find the total energy dissipated by R. Compare
with your answer from (b).