Unit 10: Inductance and Oscillating Circuits
A coil that resists its own current changing, the energy it banks in its field, and what happens once that energy sloshes back and forth with a capacitor.
6 topics · 22 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Mutual Inductance
- How it worksHow does one coil's changing flux linking a second coil define the mutual inductance between them?
- Worked exampleFind the emf induced in a secondary coil with mutual inductance 0.02 henries if the primary current changes at 50 amps per second.
- Ties togetherHow does mutual inductance generalize Faraday's law from a single loop to a pair of coupled coils?
Your turn1 of 2
Find the emf induced in a secondary coil with mutual inductance 7 times 0.01 henries if the primary current changes at 133 amps per second.Self-Inductance and Inductors
- How it worksHow does a coil's own changing flux induce a back emf that opposes changes in its own current?
- Worked exampleFind the self-inductance of a coil that develops a 6 volt back emf when its current changes at 3 amps per second.
- Common mistakeWhy doesn't an inductor oppose a steady, unchanging current the way an ordinary resistor would?
- Going furtherWhat happens to an inductor's back emf as the current through it is switched off more and more abruptly?
Your turn1 of 2
Find the self-inductance of a coil that develops a 14 volt back emf when its current changes at 13 amps per second.Energy Stored in a Magnetic Field
- How it worksHow does the work done against an inductor's own back emf become energy stored in its magnetic field?
- Worked exampleFind the energy stored in a 0.5 henry inductor carrying a current of 4 amps.
- Ties togetherHow does an inductor's energy formula mirror the one half C V squared formula that a capacitor obeys?
Your turn1 of 2
Find the energy stored in a 14 times 0.1 henry inductor carrying a current of 13 amps.LR Circuit Transients
- How it worksHow does an inductor's back emf slow a current's rise until it approaches its final value exponentially?
- Worked exampleFind the current in an LR circuit 0.01 seconds after closing the switch, with a 10 volt battery, 5 ohm resistor, and 0.02 henry inductor.
- Worked exampleFind how long it takes that same circuit's current to decay to half its starting value once shorted.
- Going furtherWhat happens to how quickly current rises and falls in an LR circuit if the inductance is made much larger?
Your turn1 of 2
Find the current in an LR circuit 15 milliseconds after closing the switch, with a 18 volt battery, a 13 ohm resistor, and a 19 times 0.1 henry inductor.Oscillations in an LC Circuit
- How it worksHow does energy trade back and forth between a capacitor's electric field and an inductor's magnetic field in an LC circuit?
- Worked exampleFind the oscillation frequency of an LC circuit with a 2 microfarad capacitor and a 50 millihenry inductor.
- Common mistakeWhy doesn't an ideal, resistance-free LC circuit's oscillation ever lose amplitude or die out on its own?
- Going furtherWhat happens to an LC circuit's oscillation frequency if its capacitance is made four times larger?
- Worked exampleFind the maximum current in an LC circuit with a 5 microfarad capacitor charged to 12 volts and a 20 millihenry inductor.
Your turn1 of 2
Find the oscillation frequency of an LC circuit with a 14 microfarad capacitor and a 132 millihenry inductor.The RLC Series Circuit
- How it worksHow does resistance drain energy out of an RLC circuit's own oscillation on every single cycle, damping it down?
- Worked exampleFind whether an RLC circuit with R = 100 ohms, L = 0.01 henries, and C = 1 microfarad is underdamped, using the damping condition.
- Going furtherWhat happens to an RLC circuit's oscillations as its resistance is increased past the critical damping value?
Your turn1 of 2
Find the critical damping resistance of an RLC circuit with L = 141 millihenries and C = 13 microfarads, the boundary between underdamped and overdamped behavior.