Chapter 11 Review
Key Terms
henry (H)
unit of inductance, ; it is also expressed as a volt second per ampere
inductance
property of a device that tells how effectively it induces an emf in another device
inductive time constant
denoted by , the characteristic time given by quantity of a particular series circuit
inductor
part of an electrical circuit to provide self-inductance, which is symbolized by a coil of wire
LC circuit
circuit composed of an ac source, inductor, and capacitor
magnetic energy density
energy stored per volume in a magnetic field
mutual inductance
geometric quantity that expresses how effective two devices are at inducing emfs in one another
RLC circuit
circuit with an ac source, resistor, inductor, and capacitor all in series.
self-inductance
effect of the device inducing emf in itself
Key Equations
| Mutual inductance by flux | |
| Mutual inductance in circuits | |
| Self-inductance in terms of magnetic flux | |
| Self-inductance in terms of emf | |
| Self-inductance of a solenoid | |
| Self-inductance of a toroid | |
| Energy stored in an inductor | |
| Current as a function of time for a circuit | |
| Time constant for a circuit | |
| Charge oscillation in circuits | |
| Angular frequency in circuits | |
| Current oscillations in circuits | |
| Charge as a function of time in circuit | |
| Angular frequency in circuit |
Summary
11.1 Mutual Inductance
- Inductance is the property of a device that expresses how effectively it induces an emf in another device.
- Mutual inductance is the effect of two devices inducing emfs in each other.
- A change in current in one circuit induces an emf in the second:
where is defined to be the mutual inductance between the two circuits and the minus sign is due to Lenz’s law.
- Symmetrically, a change in current through the second circuit induces an emf in the first:
where is the same mutual inductance as in the reverse process.
11.2 Self-Inductance and Inductors
- Current changes in a device induce an emf in the device itself, called self-inductance,
where is the self-inductance of the inductor and is the rate of change of current through it. The minus sign indicates that emf opposes the change in current, as required by Lenz’s law. The unit of self-inductance and inductance is the henry (), where
- The self-inductance of a solenoid is
where is its number of turns in the solenoid, is its cross-sectional area, is its length, and is the permeability of free space.
- The self-inductance of a toroid is
where is its number of turns in the toroid, and are the inner and outer radii of the toroid, is the height of the toroid, and is the permeability of free space.
11.3 Energy in a Magnetic Field
- The energy stored in an inductor is
- The self-inductance per unit length of coaxial cable is
11.4 RL Circuits
- When a series connection of a resistor and an inductor—an circuit—is connected to a voltage source, the time variation of the current is
(turning on),where the initial current is - The charac