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.
Differentiate: This is my guess but I have confused myself
v = V - Ve^(-t/T).
the first term in this difference disappears in the derivative, so only have to took 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.
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.
Differentiate: This is my guess but I have confused myself
v = V - Ve^(-t/T).
the first term in this difference disappears in the derivative, so only have to took 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.