RC and RL Circuits
Study Guide
Exponential Functions
In physics, most exponential functions are governed by a time constant 7 which has units of time.
The following graph shows a typical exponential decay:
C œ C! />Î7
(Exponential Decay)
Sometimes an exponential function approaches an equilibrium value Cmax . In this case, it is the
difference Cmax  C that decays exponentially:
Cmax  C œ Cmax />Î7
(Approaching Cmax )
In some cases, it may also help to use the following derivative formula:
. E>
/
œ E/E>
.>
Outline
Section 28.7: RC Circuits
A RC circuit is a circuit with a resistor and a capacitor. It may also have a battery or other
voltage source. The current in an RC circuit always dies away over time:
M œ M! />Î7
where
7 œ VG
For an RC circuit without a battery, the voltage ?Z across the capacitor and the charge U stored
in the capacitor will die away with time as well. For a circuit with a battery, ?Z and U will
instead approach some equilibrium values.
Problems: Chapter 28 # 72, 75, 82, 101
Answers: 72. (&! kH
82. "# kH
Section 31.6. RL Circuits
An RL circuit is a circuit with a resistor and an inductor. It may also have a battery or other
voltage source. The emf across the inductor in an VP circuit always dies away over time:
X œ X! />Î7
where
7œ
P
V
For an RL circuit without a battery, the current through the circuit dies away with time as well.
For a circuit with a battery, the current will instead approach some equilibrium value.
Problems: Chapter 31 # 60, 63, 85
Answers: 60. (a) M œ ! A; M œ #% mA; M œ $) mA (b) Mmax œ '! mA (c)
.M
œ $Þ! AÎs
.>