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

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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)

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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:

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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

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, 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.

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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

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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

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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

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