Transcript Electric Potential - McMaster Physics and Astronomy

Self-Inductance and Circuits
• Inductors in circuits
• RL circuits
Self-Inductance
Self-induced emf:
dI
 L  L
dt
Potential energy stored in
an inductor:
I
U L  LI
1
2
2
RL circuits: current increasing
The switch is closed at t =0;
Find I (t).
Kirchoff’s loop rule:
dI
 L
 IR  0
dt
dI   IR R  



  I
dt
L
LR

I
ε
L
R
Solution
I (t ) 



1 e
R
t /
Time Constant:
L
 
R
Note that H/Ω = seconds
(show as exercise!)
Time Constant:
 
L
R
Current Equilibrium Value:
I (t ) 
I 


R


1 e
R
t /
ε/R
63%
I
t
0
1τ
2τ
3τ
4τ
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.
I
L
R
I (t )  I o e  t / 
Current decreasing:
Time Constant:
L
 
R
I
Io
0.37 I0
0τ
τ
2τ
3τ
4τ
t
Example 2:
I1
6Ω
I3
I2
12 V
50kΩ
200 mH
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
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