Wednesday, June 28, 2006 - my son's 4th birthday!

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Chapter 21 - Electrical Current and DC circuits

Electric current is the flow of electric charge.  I = dQ/dt.   Physicists define the direction of the current in terms of positive charges (consistent with the direction of the electric field), even though it is negatively-charged electrons that flow in most situations.  Incidently, electrical engineers define current (J not I) to be in the opposite direction.
    1 A = 1 ampere = 1 amp = 1 C/s
    Typical currents in common electrical devices.
When a switch is closed so that current can flow in a circuit, the reponse is very fast (approximately the speed of light), but the average speed of a typical electron is much slower.  Why?  Approximately how slow?
Demo:  Rubber ball model of current.
    What could be done to increase the current in this demonstration?  What are the corresponding parameters to resistance?
Prob. 21.6:  What incorrect assumption is made in this problem that asks about the amount of current flowing through a TV? [assumes DC]
Many batteries are rated in mA-h.  What does this unit represent? [total amount of charge (see also CQ21.5)]
When we pay for electricity in units of kW-h, what are we really paying for? [energy (but we expect a minimum amount of power)]
Electrical resistance in a wire depends on the resistivity of the conductor, the length of the wire, and its cross-sectional area:  R = rL/A
Ohm's law is a useful relation that is valid for many (but not all) resistive loads:  V = IR, or more properly, I = V/R (Why is this form better?)
Prob. 21.12:  Find the potential difference between the feet of a bird sitting on a high-voltage power line. 
    V = IR = IpL/A = 2.5 mV, which increases with L (separation between bird's feet)
The resistivity of most metals increases with temperature (ex. tungsten), but there are exceptions (ex. carbon and other semiconductors).
    Application:  Thermal resistors (thermistors) are used in digital thermometers.
    Superconductivity - below a certain critical temperature, Tc, certain materials have zero resistance.
Exercise:  Sketch and label a graph of current as a function of voltage (I-V plot) for a light bulb that has a cold resistance of 10 ohms and a hot resistance of 100 ohms at its operating voltage of 12 V.
Electric power is the rate at which energy must be supplied:  P = IV = I*I*R = V*V/R

Resistors in series (end to end):  Req = R1 + R2 + ...
Resistors in parallel (same voltage):  1/Req = 1/R1 + 1/R2 + ...
Prob. 21.82:  If a wire of resistance R is cut into three equal lengths and connected in parallel, what is Req?
Ponderable:  How would you combine three resistors (50, 150, and 200 ohms each) to yield Req = 100 ohms?
Prob. 21.30:  To yield 150 ohms total resistance, combine the 92-ohm resistor in series with the 220 and 79-ohm resistors in parallel.
Demo:  series and parallel circuits with three 6-V batteries and 12-W bulbs rated at 12.8 V.
    What happens when a bulb is removed from either circuit?
    Why is the 8W bulb brighter than the other bulbs in the series circuit, but dimmest in the parallel circuit?
    What is the operating resistance for each bulb?  R = V*V/R = (12.8 V)^2/(12 W) = 13.6 ohms
    For four bulbs in series:  Vt = 15.7 V, I = 0.51 A, therefore Rt = (15.7 V)/(0.51 A) = 31 ohms or 7.7 ohms/bulb
    For three bulbs in series:  Vt = 10.0 V, I = 2.5 A, therefore Rt = (10.0 V)/(2.5 A) = 4 ohms or 12 ohms/bulb
    Find the internal resistance of each battery.  Rin = (emf - V)/I - (17.7 - 10.0)/(2.5 A) = 3.1 ohms or ~1 ohm/battery
Ponderable:  Which has more resistance:  a standard light bulb rated at 60 W or one rated at 100 W?  If these two bulbs were connected to a DC power supply, which one would be brighter?
Kirchhoff's Rules:
    Junction rule (conservation of charge): Total current into a junction must equal total current out.
    Loop rule (conservation of energy):  Sum of potential differences around any loop must be zero.
Capacitors in series (same charge):  1/Ceq = 1/C1 + 1/C2 + ...
Capacitors in parallel (same voltage):  Ceq = C1 + C2 + ...
Capacitors require a certain amount of time to charge and discharge. 
This time is characterized by the time constant:  tau = RC, which is the time for a capacitor to reach 63% of its maximum charge.
Prob. 51, and Active Example 21-2: Find the current through each resistor.
Prob. 21.68:  Find the time for a capacitor to be charged to 50% of its maximum value.  Find the time until the current drops to 10% of its initial value.
a) t = RCln2.0  b) t = RCln10
Prob. 21.78:  When is the current largest in an RC circuit:  immediately after the switch is closed or a long time later?
a)  I = 0.82 A,  b)  I = 0.54 A
Prob. 21.60:  The initial charge on the 11.2 uF capacitor is 134 uC.  After the switch is moved to position B, Qi will be shared between the two capacitors that have the same voltage:  Qi = Q1 + Q2, V1 = V2 = Q2/C2 = 6.49 V.
Prob. 21.81:  Find the resistance needed in a pacemaker operating with a 9.0V-battery to yield 75 pulses/minute when the 110 uF capacitor charges to 0.25 V.

Review of Conceptual Questions from HW21a, especially: CQ10, 18, 26, 42.
Correct this statement:  "Resistors in parallel have the same potential difference through them."

Concept Tests (use phys25 username and password to access)