Calculus
I have recently been given the following question but I have no idea how to differntiate the equation or plot the equations. Can you please help me?
Capacitor = 100 nF
Resistor = 47 kΩ
Supply voltage = 5 V
Charging characteristic for a series capacitive circuit:
v=V(1- e-^(1/T)) where T=CR
n Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds).
n Differentiate the charging equation and find the rate of change of voltage at 6 ms.
hint on how to differentiate the equation: V and T are constants. we can re-write the equation as:
v = V - Ve^(-t/T).
the first term in this difference disappears in the derivative, so we only have to take the derivative of -Ve^(-t/T).
the -V in front is just a constant, so v'(t) = (-V)(d/dt)(e^(-t/T))
and e^(-t/T) is of the form e^(at), where in this particular case, a = -1/T.
Skeeter: Thanks, I made a spelling mistake
Question: Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds)
T=CR
T=0,1 x 47000
t=0.00470
Answers:
T v=V(1- e-^(t/T)) How can I draw the spreadsheet when answers =5?
0 v=5(1- e-^(0/T)) 0
1 v=5(1- e-^(1/T)) 5
2 v=5(1- e-^(2/T)) 5
3 v=5(1- e-^(3/T)) 5
4 v=5(1- e-^(4/T)) 5
5 v=5(1- e-^(5/T)) 5
6 Etc,
..
...
...
20 v=5(1- e-^(20/T)) 5
Deveno: Cheers for the hints
sure ...
... and so on. You should do some research on how to do it in a spreadsheet ...
how to generate a graph in excel - Google Search