Download dy` -+4y=8

Lesson 14
(1) For the differential equation
dy'
-+4y=8
dx
1.
2.
3.
4.
Write the general solution of the homogeneous part
Find a particular solution
Write the general solution
Write the solution with initial condition y(O)=l.
(2)A capacitor with C=2.0flFis fully charged with a 12Vbattery, and then
discharged through a 4.00 resistor. Find how long it takes
1.
2.
for the voltage to reach 2.0V
for the stored energy to become halved
(3) Repeat Problem (2) if the resistor is 8.00.( calculation not needed)
(4) Acapacitor with C=2.0Fis charged with a 12Vbattery through a 4.00 resistor,
starting with no charge on it.
1.
2.
3.
4.
5.
What is the charge at t=oo?
Write an expression for the charge Q at time t.
What is the current at t=O?
What is the current at t=oo?
What is the current at t=8.0s?
(5) Switch S in the circuit is opened after having been closed for a
long time. 4.00s later the voltage drop across the resistor is
20.0V.Find R.
(6) Switch S has been open for a long time. At time t=O,it is then
closed. Find the battery current
1.
2.
just after S is closed
a long time after S is closed
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