# Math question

• Dec 15th 2009, 09:33 PM
angelofmusic
Math question
A RLC circuit consisted of a resistor R, a capacitor C, and an inductor L connected in series together with a switch and voltage source E. Prior to closing switch at start, there is no current and no charge on the capacitor. Determine the charge q(t) on the capacitor and current i(t) in the circuit at time T. Given that R=160ohms, L= 1H, C = 10^-4 F, E=20V

1a) kirchoff's law
b) the formulae for voltage drop across R, L, C
c) Relationship between charge and current
2) Apply the above to obtain a differential equation for charge
3) state the initial condition
4) use laplace transform to solve the differential equation to find charge
5) use your result to find current
• Dec 17th 2009, 11:47 PM
Kiwi_Dave
Quote:

Originally Posted by angelofmusic
A RLC circuit consisted of a resistor R, a capacitor C, and an inductor L connected in series together with a switch and voltage source E. Prior to closing switch at start, there is no current and no charge on the capacitor. Determine the charge q(t) on the capacitor and current i(t) in the circuit at time T. Given that R=160ohms, L= 1H, C = 10^-4 F, E=20V

1a) kirchoff's law
b) the formulae for voltage drop across R, L, C
c) Relationship between charge and current
2) Apply the above to obtain a differential equation for charge
3) state the initial condition
4) use laplace transform to solve the differential equation to find charge
5) use your result to find current

1a. Using Kirchoff's law:
$\displaystyle E=V_r+V_l+V_c$

1b. The voltages accross these passive components are:
$\displaystyle V_r=iR$
$\displaystyle V_l=\frac{di}{dt}L$
$\displaystyle V_c=C \int i dt$

So using 1a
$\displaystyle E=iR+\frac{di}{dt}L+C \int i dt$

It looks like the parts of the question above lead you step by step to the answer.