Chapter 6 RL and RC Circuits
Inductors and Capacitors Energy Storage Components Voltages and currents are related through calculus rather than ohm’s law – But KCL and KVL always apply at each instant Resistors gave us static circuit behavior Now we have dynamic currents and voltages changing over time You may find a plotting calculator, or MATLAB to be very helpful in visualizing the variables
How they work Inductor—Wire wrapped around magnetic core, current flow induces magnetic field, which dynamically induces voltage drop Capacitor—Two metal plates separated by a film, voltage applied causes “displaced current” to accumulate on plates
Energy is stored Inductors store energy – Coil (inductor) in your car fires spark plugs at right moment Capacitors store energy – Capacitor in your camera stores energy from batteries to fire flashbulb when picture is taken. They can only release what has been stored – Can’t generate energy – They are passive components similar to resistors
R, L, C Comparison
5.1 Inductors A time-varying current source is applied across an inductor. Using the basic mathematical model, – What is the resulting voltage across the inductor vs time? – What is the power, energy, etc, vs time? – What if a time-varying voltage source is used instead? – To solve—determine which formula applies, then apply it.
5.2 Capacitors A time-varying voltage source is applied across a capacitor. Using the basic mathematical model, – What is the resulting current across the capacitor vs time? – What is the power, energy, etc, vs time? – What if a time-varying current source is used instead? – To solve—determine which formula applies, then apply it.
Series and Parallel combinations Inductors are like resistors as far as series and parallel combinations Capacitors are the opposite of resistors in terms of how they combine
5.4 Natural Response These are circuits that have been “charged up” by an external source, which is removed at t=0 We simply calculate the dissipation of the stored energy into the rest of the circuit