4. The R-L Circuit
0di
iR Ldt
E
di Ri
dt L L
E
dq q
dt RC R
E
0q
iRC
E
/( ) (1 )t RCq t C e E
R-C circuit
( / )1 R L ti eR
E
Current Growth
Problem 30.64) Find the reading in each ammeter and voltmeter at the following times
a) just after switch S is closed
b) after S has been closed a very long time.
Problem 30-65) Switch S is closed at t=0 with no charge initially on the capacitor.
a) Find the reading of each ammeter and each voltmeter just after S is closed.
b) Find the reading of each ammeter and each voltmeter after a long time has elapsed.
c) Find the maximum charge on the capacitor.
5. L-C Circuit Oscillating L-C circuit
Applet http://www.walter-fendt.de/ph11e/osccirc.htm http://physics.bu.edu/~duffy/semester2/c19_LC.html
Electrical oscillation
0di q
Ldt C
2
2
10
d qq
dt LC
2
20
d x kx
dt m
( ) cos( )q t Q t
Simple Harmonic oscillation
1
LC
Example 30.9) 300 V was charged to a 25F capacitor. Then, disconnected from power, connected to 10 mH inductor. Find
a) frequency and period
b) charge and current at t=1.2 ms.
Example 30.10) Find the magnetic and electric energy of the circuit of Example 30.9).
a) t=0, b) t=1.2 ms
Problem 30.34) An L-C circuit. When i=Imax , find
a) Maximum energy stored in the capacitor
b) How often you will have that energy?
6. L-R-C circuit
L-R-C circuit
Underdamped oscillation solution
0di q
iR Ldt C
2
2
10
d q R dqq
dt L dt LC