FACULTY OF SCIENCE, WINTER 2008
PHYS 126 LEC B3 : Fluids, Fields and Radiation (Instructor: Marc de Montigny)
Walker, Physics, Chapter 21: Electric Current and Direct-Current Circuits
- Section 21-1: Electric Current
- P. 696, Eq. 21-1, I = ΔQ/Δt. ΔQ is the amount of charge flowing past a given point in a wire in a time Δt.
- P. 696, SI Unit: 1 ampere or amp (A) = 1 C/s.
- The direction of I is given by the direction of motion of positive test charges, as shown in Figure 21-4.
- DC circuits (direct-current) : the current always flows in the same direction.
- AC circuits (alternating-current) : currents periodically reverse their direction. Further discussed in Chapter 24.
- Electromotive Force
- P. 697, Electromotive force (emf, ε) is the potential difference between the two terminals of an ideal battery. The potential difference V between the terminals of a real battery is usually less that ε, as discussed in P. 707.
- A source of emf maintains a potential difference usually due to non-electrical (e.g. chemical, magnetic, solar cells, fuel cells, nuclear) sources.
- In spite of its name, emf is NOT a force. The unit of emf is Volt.
- This figure shows the symbol for a battery, or source of emf, where the longer terminal corresponds to a higher potential, and the shorter terminal has a lower potential, i.e. VA < VB.
- Note that current does not necessary flow from - to + . An example is if a system consists two batteries with opposing polarities. This is analogous to forces: the acceleration does not necessarilly points in the direction of the force.
- P. 698, Figure 21-3 illustrates a mechanical analogy of the circuit in Figure 21-4: the person lifting the water corresponds to the source of emf and the paddle corresponds to the lightbulb (or resistance) which dissipates power. Just like this person performs some work to lift the water, when an ideal battery moves a charge ΔQ around a circuit, it performs a work W = ΔQε. This figure showing the analogy with water will be useful when we discuss resistors in parallel and in series.
- P. 726, Problem 7
- Section 21-2: Resistance and Ohm's Law
- P. 699, Eq. 21-2, Ohm's Law: V = RI.
- R is the resistance. Unit: 1 ohm (Ω) = 1 V/A.
- This figure shows the symbol for a resistance. The electric potential decreases as one moves across a resistor in the direction of the current, i.e. VC > VD. (See top of P. 712.)
- This figure shows that a graph of V as a function of I is a line with slope R.
- Ohm's Law is not universal; it is valid only for so-called ohmic materials. Yet, nonohmic materials can be quite useful, e.g. Light-Emitting Diodes (LEDs). It is not a law of Physics, like conservation of energy.
- This figure shows resistors similar to the ones used in your lab experiments. Resistor Color Code Converter [No need to memorize that, of course.]
- Simple simulation
- P. 700, Eq. 21-3, Resistivity ρ defined by R = ρL/A.
- SI Unit of ρ is Ω•m.
- Some resistivities are listed in Table 21-1.
- [Omitted: For many materials, resistivity depends on temperature as follows: ρ = ρ0 (1 + α ΔT), where α is called the temperature coefficient of resistivity, and ρ0 is another coefficient which depends on the material.
- P. 726, Problem 14
- P. 726, Problem 17
- P. 726, Problem 73
- P. 727, Problem 18
- Section 21-3: Energy and Power in Electric Circuits
- P. 702, Eq. 21-4, Electrical Power: P = IV. [Unit of P, watt (W)]
- Eq. 21-4 follows from P = ΔU/Δt where ΔU is the change of potential energy when a charge ΔQ moves across a potential difference V. Then P = ΔQ V/Δt = IV.
- P. 703, Eq. 21-5, P = I2 R (ohmic material)
- P. 703, Eq. 21-6, P = V2/R (ohmic material)
- P. 727, Problem 22
- P. 727, Problem 25
- Section 21-4: Resistors in Series and Parallel
- Resistors in series:
- P. 706, Eq. 21-7, Resistors in series: Req = R1 + R2 + ...
- P. 706, Figure 21-6 illustrates the resistance Req equivalent to three resistors.
- This figure illustrates the analogy between waterfalls and two resistors in series.
- The same current I flows through each resistor in series. The potential differences add up.
- Note that for resistors in series, Req is greater than the largest resistance in the combination, that is, it increases the resistance.
- Resistors in parallel:
- P. 708, Eq. 21-10, Resistors in parallel: 1/Req = 1/R1 + 1/R2 + ...
- P. 708, Figure 21-9 illustrates the resistance Req equivalent to three resistors.
- This figure illustrates the analogy between waterfalls and two resistors in series.
- Resistors in parallel are connected across the same potential difference.
- Note that for resistors in parallel, Req is smaller than the smallest resistance in the combination, that is, it reduces the resistance.
- P. 728, Problem 43
- P. 707, Figure 21-7 illustrates an important example of resistors in series: the internal resistance r of a real battery. This accounts for the internal losses and case the potential difference between the terminals to be less than the emf ε and to depend on the current in the battery.
- Starting a Car With Flashlight Batteries
- Section 21-5: Kirchhoff's Rules
- P. 711, Kirchhoff's Rules
- Junction Rule: The algebraic sum of all currents at any junction in a circuit must equal zero. 'Algebraic' means that incoming and outgoing currents carry different sign. This rule is a consequence of the conservation of charge.
- Loop Rule: The algebraic sum of all potential differences around any closed loop in a circuit must equal zero. 'Algebraic' means that the sign of potential difference depends on whether it increases or decreases in the direction of motion around the circuit. This rule is a consequence of the conservation of energy.
- P. 728, Problem 48
- P. 728, Problem 50
- Effects of Current on Human Body
- Section 21-6: Circuits Containing Capacitors
- P. 714, Capacitors in Parallel
- P. 714, Figure 21-17
- P. 714, Eq. 21-14: Ceq = C1 + C2 + ...
- Each capacitor has the same potential difference. The total charge is the sum of the charges.
- P. 716, Capacitors in Series
- P. 716, Figure 21-18
- P. 716, Eq. 21-10, Capacitors in series: 1/Ceq = 1/C1 + 1/C2 + ...
- The capacitors have the same charge. The potential differences are added up.
- P. 729, Problem 58
- P. 729, Problem 60
- Additional Problem
- Section 21-7: RC Circuits
- Charging a Capacitor
- P. 717, Figure 21-19 shows an RC circuit. Figure 21-20 shows the charge versus time.
- P. 717, Eq. 21-18, Charging Capacitor: q(t) = Cε (1 - e-t/RC)
- RC is usually named 'time constant of the circuit' and it is denoted by the greek letter tau, τ (same symbol as torque, in PHYS 124).
- P. 718, Eq. 21-19, Current in a charging capacitor: I(t) = (ε/R) e-t/RC
- Discharging a Capacitor
- P. 719, Figure 21-22 shows an RC circuit, where the battery has been removed and the capacitor is discharging. Figure 21-21 shows the current versus time. Note that the charge has the same behaviour.
- P. 719, Eq. 21-20, Discharging Capacitor: q(t) = Q e-t/RC
- P. 729, Problem 62
- P. 731, Problem 96
- Section 21-8: Ammeters and Voltmeters
- P. 720: An ammeter is connected in series with the section of the circuit in which the current is to be measured. An ideal ammeter has an internal resistance equal to zero. P. 720, Figure 21-23.
- P. 720: A voltmeter is connected in parallel with the portion of the circuit in which the potential difference is to be measured. An ideal voltmeter has an internal resistance which is infinite. P. 720, Figure 21-24.