RC Circuits Charging and discharging and calculus! Oh, my!

Recall  Capacitors are charge storage devices. C=Q/V  Current is the rate at which some amount of charge is moved in a circuit. i = dQ/dt  Ohm’s Law describes the relationships between voltage and current. v=ir  Kirchhoff rules! (KVL and KCL)

Charging an RC circuit  Switch closes at t=0  As cap charges, amount of current flowing in circuit changes (increases or decreases? Why?)  Applying KVL:

We’re not in Kansas any more, Toto Initially, there is no charge stored on the cap. After a long time, it is fully charged and q=CV battery. has a solution of the form and the values of the constants depend on the charge in the circuit at and

, the time constant  Tau describes the characteristic period over which stuff of significance happens in the circuit.  It depends on the sizes of the components in the circuit.  =RC  3  is considered the steady-state condition. By this time, system parameters have reached 95% of their final value.

Charging an RC circuit from

What does this mean, Oh Great and Powerful Oz?  Initially, cap acts like a wire. After a long time (t>3) it acts like an open circuit. i asymptotically decreases to zero Q stored asymptotically increases to CV battery V cap approaches V battery

Discharging the RC From