1. Self-Inductance and Circuits
Inductors in circuits
RL circuits

2. Self-Inductance Self-induced emf: I
Potential energy stored in an inductor:

3. ε RL circuits: current increasing The switch is closed at t =0; I
Find I (t). I ε L
Kirchoff’s loop rule: R

4. Solution
Time Constant:
Note that H/Ω = seconds
(show as exercise!)

5. Time Constant: Current Equilibrium Value:
τ τ τ 4τ
63%
ε/R

6. Example 1
Calculate the inductance in an RL circuit in which R=0.5Ω
and the current increases to one fourth of its final value
in 1.5 sec.

7. RL circuits: current decreasing
Assume the initial current I0 is known. Find the differential equation for I(t) and solve it.

8. Current decreasing:
Time Constant: I Io
0.37 I0 t
0τ τ τ τ 4τ

9. Example 2: I3 I2 I1 6Ω
12 V
50kΩ
200 mH
The switch has been closed for a long time. Find the current through each component, and the voltage across each component.
The switch is now opened. Find the currents and voltages just afterwards.

10. Solution

11. Example 3
At t = 0, an emf of 500 V is applied to a coil that has an inductance of H and a resistance of 30.0 Ω. a) Find the energy stored in the magnetic field when the current reaches half its maximum value. b) After the emf is connected, how long does it take the current to reach this value?

12. Solution