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RC Circuits

RC Circuits. Charging and discharging and calculus! Oh, my!. Recall. Capacitors are charge storage devices. C=Q/ D V Current is the rate at which some amount of charge is moved in a circuit. i = dQ/dt

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RC Circuits

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

  2. Recall • Capacitors are charge storage devices. C=Q/DV • 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. Dv=ir • Kirchhoff rules! (KVL and KCL)

  3. 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:

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

  5. t, 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. t=RC • 3t is considered the steady-state condition. By this time, system parameters have reached 95% of their final value.

  6. Charging an RC circuit from http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capchg.html#c1

  7. What does this mean, Oh Great and Powerful Oz? • Initially, cap acts like a wire. After a long time (t>3t) it acts like an open circuit. • i asymptotically decreases to zero • Qstored asymptotically increases to CVbattery • Vcap approaches Vbattery

  8. Discharging the RC From http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capdis.html#c2

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