RC Circuits - University Of Illinois
[Pages:22]Physics 102: Lecture 7
RC Circuits
Physics 102: Lecture 7, Slide 1
RC Circuits
? Circuits that have both resistors and capacitors:
RK
RNa
RCl
C
K + Na
Cl +
+
S
? With resistance in the circuits, capacitors do not charge and discharge instantaneously ? it takes time (even if only fractions of a second).
Physics 102: Lecture 7, Slide 2
RC Circuits
Used to controllably store and release energy
Today:
? RC Circuits ? Charging Capacitors ? Discharging Capacitors ? Intermediate Behavior
Physics 102: Lecture 7, Slide 3
Charging Capacitors
Storing energy to use later
? Capacitor is initially uncharged and switch is open. Switch is then closed.
? What is current I0 in circuit immediately thereafter?
? What is current I in circuit a long time later?
Physics 102: Lecture 7, Slide 4
C
R
S
Charging Capacitors: t = 0
? Capacitor is initially uncharged and
C
switch is open. Switch is then closed.
R
? What is current I0 in circuit immediately
thereafter?
S
? Capacitor initially uncharged
? Therefore VC =0 (since V=Q/C)
R
? Therefore C behaves as a wire (short
circuit)
? Ohm's law!
I0 = /R
Physics 102: Lecture 7, Slide 5
Charging Capacitors: t > 0
? I0 = /R
? Positive charge flows
? Onto bottom plate (+Q) ? Away from top plate (-Q)
-C
R
+
? As charge builds up, VC rises (VC=Q/C)
? Loop: ? VC ? I R = 0
? I = ( ? VC)/R ? Therefore I falls as Q rises
? When t is very large ()
- --
R
++ +
? I = 0: no current flow into/out of
capacitor at long times
? VC =
Physics 102: Lecture 7, Slide 6
ACT/CheckPoint 1
Both switches are initially open, and the capacitor is uncharged.
What is the current through the battery just after switch S1 is closed?
+ 2R -
1) Ib = 0
2) Ib = E /(3R)
Ib
3) Ib = E /(2R)
4) Ib = E /R
+
+
C
-
R
-
Capacitor acts like a wire the instant the switch is closed:
S2 S1
I = E /(2R)
Physics 102: Lecture 7, Slide 7
ACT/CheckPoint 3
Both switches are initially open, and the capacitor is uncharged.
What is the current through the battery after switch 1 has been
closed a long time?
+ 2R -
1) Ib = 0 3) Ib = E/(2R)
2) Ib = E/(3R)
Ib
4) Ib = E/R
+
-
+
C
-
R
S2 S1
? Long time current through capacitor is zero ? Ib=0 because the battery and capacitor are in series.
? KLR: E ? 0 ? q/C = 0 q = E C
Physics 102: Lecture 7, Slide 8
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