Self-Inductance and Circuits Inductors in circuits RL circuits

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

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

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

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

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

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.

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.

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

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.

Solution

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

Solution

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

Solution