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

2. Inductors in Series and Parallel L T = L 1 +L 2 …. 1/L T = 1/L 1 + 1/L 2 …

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

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

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

6. 0 1τ 2τ 3τ 4τ 63% ε /R I t Time Constant: Current Equilibrium Value:

7. 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.

8. L R I RL circuits: current decreasing Assume the initial current I 0 is known. Find the differential equation for I(t) and solve it.

9. I t 0τ τ 2τ 3τ 4τ 0.37 I 0 IoIo Current decreasing: Time Constant:

10. Example 2: 12 V 200 mH 50kΩ 6Ω I3I3 I2I2 I1I1 a)The switch has been closed for a long time. Find the current through each component, and the voltage across each component. b)The switch is now opened. Find the currents and voltages just afterwards.

11. Solution

12. LC circuits (Extra! – not on test/exam) The switch is closed at t =0; Find I (t). C L I Which can be written as (remember, P=VI): + - Looking at the energy loss in each component of the circuit gives us: E L +E C =0

13. Solution

14. RLC circuits (Extra! – not on test/exam) The switch is closed at t =0; Find I (t). C L R I Which can be written as (remember, P=VI=I 2 R): + - Looking at the energy loss in each component of the circuit gives us: E L +E R +E C =0

15. Solution