Chapter 25 Current, Resistance, and Electromotive Force PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun
Main points (I, R, emf) 1. If a constant potential difference(pd) is applied across a conductor, electrons accelerate in the electric field but eventually reach a terminal (drift) velocity v due to drag friction from collisions. Current I=dq/dt=n q va [unit = Ampere=A](n=density of charge carriers), conventionally in the direction of flow of +ve charges. Current density J=I/A=n q v (vector: J=nqv). 2. Ohm s law: In metals, J=σE (σ=conductivity, resistivity ρ=1/ σ). J=I/A and E=dV/dL=V/L and so V=IR where R= ρ/a dl = ρl/a. Resistance R increases with temperature T [average KE of random motion] like resistivity. In a local approximation ρ(t)= ρ _0(1+α(T-T_0)). (T T 0)) 3. For current to continue flowing, one needs a closed path (complete circuit). The work done, by some source device in a closed circuit, to move a unit positive charge through the closed circuit is called the electromotive force ε (emf) of the device. If the device has an internal resistance r, then the actual potential difference across its terminals is V=ε-Ir. 4. Circuit symbols/conventions [Resistors, emf sources, capacitors, inductors, Voltmeters, Ameters, ]. 5. The power=d(energy)/dt delivered by (or delivered to) any device in a circuit is P=IV, where V is the potential difference across the device and I is the current through the device.
Goals for Chapter 25 To consider current and current density To study the intrinsic property of resistivity To use Ohm s Law and study resistance and resistors To connect circuits (mentally, virtually, or with actual parts) and find emf To examine circuits and determine the energy and power in them To describe the conduction of metals microscopically, on an atomic scale
Introduction Electrons leave one terminal of a battery, pass through wire of low resistance, reach a light bulb with a special calibrated resistor sealed in a bulb of inert gas, and dthen return to the opposite terminal of the battery. The electron s journey has been interrupted dby our special resistor because we had a nefarious ulterior motive. We wanted light!
The direction of current flow In the absence of an external field, electrons move randomly in a conductor. If a field exists near the conductor, its force on the electron imposes a drift.
Current flowing Positive charges would move with the electric field, electrons move in opposition. The motion of electrons in a wire is analogous to water coursing through a river. This fits the metaphor used earlier.
Current flow requires conductors throughout In Figure 25.4, a negative terminal of a battery extends through wire to a bare post inside the open tube. Another open tube next to the first one also contains a bare post with wire running back to entry of a light bulb resistor. The exit of the light bulb resistor continues through wire back to the positive terminal on the battery. If the tubes are immersed in a conducting fluid, the bulb will light. If the fluid is nonconducting, the light will remain off. Consider Example 25.1.
Resistivity is intrinsic to a metal sample (like density is)
Resistivity and temperature Resistivity rises with increasing temperature. The electronic motion is analogous to shopping on quiet days (lower T) or busy days (higher T). See Figure 25.6. Table 25.2 tabulates resistivities.
Resistance is an extensive property (like mass) Copper is a good conductor, but it s still possible to add magnitudes of resistance with copper because it takes more mass. Figure 25.7 illustrates the model. Figure 25.8 shows an unfortunate example of the heat generated when current and resistance are unmatched.
Resistors are color-coded for assembly work
Current voltage relationships Ohm s Law is linear, but current flow through other devices may not be. Follow Example 25.2. 2
Calculating resistances Refer to Example 25.3 to see the effects of changing temperature. Refer to Example 25.4 to calculate the resistance of a hollow tube (unlike a normal wire). Figure 25.11 (below) illustrates this example.
Electromotive force and circuits You ve probably already thought water doesn t flow through a pipe without a pump; why should electrons flow through a wire? If those were your daydreams, you re right. See Figures 25.12 and 25.13 at right.
Ideal diagrams of open and complete circuits
Internal resistance We generalize at the outset, but the truth of a battery is that you only get 12 V when a 12 V battery isn t connected. Making a connection allows electrons to flow, but internal resistance within the battery actually delivers incrementally less than 12 V.
Symbols for circuit diagrams Shorthand symbols are in use for all wiring components. See below.
Source in an open circuit I Consider Conceptual Example 25.5. 5 This example is illustrated in Figure 25.17.
Source in an open circuit II Follow Example 25.6.
Voltmeters and ammeters Follow Conceptual Example 25.7.
A source with a short circuit Follow Example 25.8. Figure 25.20 (below) illustrates this example.
Potential changes around a circuit The net change in potential energy must be zero for the entire circuit. Local differences in potential and emf do occur. See Figure 25.21 below.
Energy conversion and power input to a source
Power and energy in circuits Consider Problem-Solving Strategy 25.1. Refer to Example 25.9, illustrated by Figure 25.25 below. Refer to Example 25.10. Refer to Example 25.11, illustrated by Figure 25.26 below.
A microscopic look at conduction Consider Figure 25.27. 27 Consider Figure 25.28. Follow Example 25.12.