1 / 16

RC Circuits

RC Circuits. circuits in which the currents vary in time rate of charging a cap depends on C and R of circuit differential equations.

orrin
Download Presentation

RC Circuits

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. RC Circuits • circuits in which the currents vary in time • rate of charging a cap depends on C and R of circuit • differential equations

  2. Quiz:After the switch is closed, the light from the bulb:A) Is brightest just after the switch is closed, then fades slowly and disappears.B) Increases gradually to maximum brightness, over a few seconds, then remains steady.C) Comes to maximum brightness immediately, and remains steady.D) The bulb remains off.

  3. I Given: R, C, qo (initial charge) Find: q(t) and I(t) when switch is closed q C R -q 1) (Kirchhoff’s Loop Rule) 2) Discharging a Capacitor (- sign because q decreases for I > 0 That is, current in circuit equals the decrease of charge on the capacitor)

  4. Combine 1) and 2) to get: I where: q = q(t) q(0) = qo q C R -q This is a differential equation for the function q(t), subject to the initial condition q(0) = q0 . We are looking for a function which is proportional to its own first derivative (since dq/dt ~ -q).

  5. Solution: RC is called the “time constant” or “characteristic time” of the circuit. Units: 1 Ω x 1 F = 1 second (show this!) Write t (“tau”) = RC, then: (discharging)

  6. q Discharging qo t 2 3 t = , q ≈ 0.37 qo = (qo/e) t = 2 , q ≈ 0.14 qo = (qo/e2) t = 3 , q ≈ 0.05 qo = (qo/e3) t  ∞ , q  0 = (qo/e∞)

  7. Draw a graph for I(t).

  8. Quiz • A capacitor is charged up to 18 volts, and then connected across a resistor. After 10 seconds, the capacitor voltage has fallen to 12 volts. • Find the time constant RC, and… • What will the voltage be after another 10 seconds (20 seconds total)? • 8V • 6V • 4V • 0

  9. Then, where t =RC. Charging a capacitor C is initially uncharged, and the switch is closed at t=0. After a long time, the capacitor has charge Qf . C R Question: What is Qf equal to?

  10. Charging a capacitor q Qf t 2 3 t = 0, q=0 t = 3 RC, q 0.95 Qf t = RC, q 0.63 Qf etc. t = 2 RC, q 0.86 Qf

  11. Draw a graph of I(t). Why is I=+dq/dt this time?

  12. Example 2 100 kΩ The capacitor is initially uncharged. After the switch is closed, find: 12 V 2 µF • Initial current • Initial voltage across the resistor • Initial voltage across the capacitor • Time for voltage across C to reach 0.63*12V • Final voltage across the resistor • Final voltage across the capacitor

  13. Solution

  14. Example:A 2kΩ and a 3kΩ resistors connected in parallel are connected in series with a 2uF and a 3uF capacitors that are connected in parallel. The power source is 120V. Find the charge on each capacitor as a function of time.

  15. Quiz:In a simple circuit with a capacitor, resistor and a switch, long time after the switch is closed, the current in the circuit will be:A) ε/RB) ε/τRC) ε/eRD) zero

  16. “RC” Circuits • a capacitor takes time to charge or discharge through a resistor • “time constant” or “characteristic time” • = RC • (1 ohm) x (1 farad) = 1 second

More Related