Presentation on theme: "RC Circuits Charging and discharging and calculus! Oh, my!"— Presentation transcript:
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 http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capchg.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capchg.html#c1
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 http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capdis.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capdis.html#c2