Hi I need to find out the answer for the following question This is one of my home work in forier series class.
An R.L.C. circuit has an emf of 100 cos2t, a resistance of 80(ohm), an inductance of 20H and capacitance of 10^-2 F. Find an expression for the charge at any time t.
The RLC circuit should be in series.
A sum of voltages is not a charge! And, more correctly, it is "voltage drop" across each component. The voltage drop across a resistance is proportional to the current: V= R i. The voltage drop across a coil is proportional to the derivative of the current: . And the voltage drop across a capacitor is proportional to the charge on the plates: .
The total voltage drop around the circuit must be equal to the emf supplied:
Also, so you can get a differential equation for i, the current in the circuit, by differentiating the whole equation with respect to t:
.
If you really are asked for the charge on the capacitor plates, solve that equation for i, then integrate to get q.
(I can't see that this has anything to do with "Fourier series".