Self-Inductance and Circuits Inductors in circuits RL circuits

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

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

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

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

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.

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

Current decreasing: Time Constant: I Io 0.37 I0 t 0τ τ 2τ 3τ 4τ

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.

Solution

Example 3 At t = 0, an emf of 500 V is applied to a coil that has an inductance of 0.800 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?

Solution