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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