# Thread: Calcu+Fourier series problem

1. ## Calcu+Fourier series problem

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.

2. Originally Posted by dhammikai
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.
The charge on what? One plate of the capacitor? A circuit does not have a specific "charge" at any time t.

3. Actally I am not sure abt that, but I am thinking the answer can be get

$\mbox{Voltage across L+Voltage across C+Voltage across R}$

But I am stuck .. how I formulate this things together...??

4. Originally Posted by dhammikai
Actally I am not sure abt that, but I am thinking the answer can be get

$\mbox{Voltage across L+Voltage across C+Voltage across R}$

But I am stuck .. how I formulate this things together...??
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: $V= L\frac{di}{dt}$. And the voltage drop across a capacitor is proportional to the charge on the plates: $V= \frac{1}{C} q$.
The total voltage drop around the circuit must be equal to the emf supplied:
$L\frac{di}{dt}+ Ri+ \frac{1}{C}q= 100 cos(2t)$

Also, $i= \frac{dq}{dt}$ so you can get a differential equation for i, the current in the circuit, by differentiating the whole equation with respect to t:
$\L\frac{d^2i}{dt^2}+ R\frac{di}{dt}+ \frac{1}{C} i= -200 sin(2t)$.

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".

5. Please give me a help to integration of q, how I start..