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