Solving non-series (L)RC problems?

[jehan60188]

Homework Statement

given circuits such as

http://img196.imageshack.us/img196/8599/48692547.gif

or

http://img854.imageshack.us/img854/1848/50833427.gif

how does one solve for voltage, current, impedance, etc?
is it a matter of kirchhoffs loop + junction rules, and differential equations?

like, what's the charge on the capacitor at time t?
or potential energy in the circuit?
or other stuff, i guess

Homework Equations

v=IR
Z = sqrt(R-(XL-XC)^2)
only for a series loop though.

The Attempt at a Solution

no idea

 

[gneill]

how does one solve for voltage, current, impedance, etc?
is it a matter of kirchhoffs loop + junction rules, and differential equations?

like, what's the charge on the capacitor at time t?
or potential energy in the circuit?
or other stuff, i guess

Yes, all the usual laws apply including KVL, KCL, etc., in order to write differential equations for the circuit which can be solved to yield what you want to find. There are some fancy techniques that you'll eventually come across (such as Laplace transforms) which will make your life much easier in the regard

When a circuit contains just one type of reactive component, L or C, then often the formal writing and solving of differential equations for the circuit can be dispensed with because the form of the solution will invariably be that of an exponential charge or discharge, and the rules of thumb for t=0, t=0⁺, t→∞ for L and C in DC circuits can set the boundaries of operation.

Homework Equations

v=IR
Z = sqrt(R-(XL-XC)^2)
only for a series loop though.

The Attempt at a Solution

no idea

Since you've got DC voltage sources you're looking for the transient response of the LC circuit, so XL and XC aren't going to do you too much good here.

You can write either loop equations or node equations that use the calculus "definitions" for the L and C components, thus resulting in the differential equations for the circuit.

 

[jehan60188]

doing practice problems was super helpful- I realized that a capacitor acts like an open wire at t=0, and an inductor acts like an open wire at t = infinity (for a DC circuit). very helpful for modelling!