Lecture 39
• RC circuits
• review of chapters 25-31 for final (see also
course webpage)
RC Circuits (I)
•
Time-dependent
currents: charging
and discharging of
capacitors
•
Analysis of RC
circuits (resistors
and capacitors):
•
Q
C
K irchho ’s loop law: ∆ V C + ∆ V R =
− IR = 0
dq (thru’ resistor) = − dQ (removed from capacitor)
Q dQ
t
dQ
Q
1
d t + R C = 0, i.e., Q 0 Q = − R C 0 dt
exponential decay
of Q, I:
I = −
I0 =
dQ
dt
Q0
RC
= I0e − t
=
∆ V0
R
I = −
dQ
dt
= RC
RC Circuits (II)
•
Example of RC circuit: position
a (long time) to position b:
what is the charge on capacitor
and current thru’ resistor at t
B at tery charges capacitor to 9 V ;
discharges thru’ resistor (ideal wires)
= R C = (10Ω) (1.0 × 10; − 6 F ) = 10 µ s
Q 0 = C ∆ V C = 9.0 µ C
/̈ = (9 . 0 µ C ) e − ( 5 . 0 µ s ) / ( 1 0 µ s )
Q = Q0e
= (9.0 µ C ) e − 0 . 5 = 5.5 µ C
I = I 0 e − t / = (0.90 A ) e − 0 . 5 = 0.55 A
•
charging of capacitor by battery
(slowing by resistor) until ∆ V C = E
(current stops): full charge of
capacitor: Q m a x = C ( ∆ V C ) m a x = C E
Q = Qmax 1 − e− t/
Review of chapters 25-31
Electrostatics
•
•
Coulomb’s law (forces between 2 point charges):
•
•
•
•
Electric Field due to point charge:
Electric Field: source charge alters space (creates “field”);
test/probe charge responds to it (
)
superposition (dipole, rod, ring, disk, plane/capacitor): Ē n e t =
motion of charge in electric field: a =
F
m
=
i
Ē i
qE
m
Gauss’s law (useful for symmetric charge distribution):
Currents
•
causes electrons to drift (on top of random motion): v d =
giving current:
;
e
m
E ,
Review of chapters 25-31 (continued)
•
•
•
•
•
Electric Potential (Energy): ∆ U e l ec = − W e l ec ( i
•
•
•
Ohm’s law:
•
f);
Electric Potential due to point charge:
Superposition (V due to ring, disk...): V =
Electric Potential and Field:
i
Vi
;
Connecting Potential and Current: battery (source of potential
difference) creates ∆ Vba t = ∆ V w i r e
Capacitance:
Combinations of Capacitors:
Energy stored in capacitor: U C =
2
0
u
=
E
in electric field: E
2
Q2
2C
=
1
2
2
C (∆V C ) ;
Review of chapters 25-31(continued)
Electric Circuits
•
Circuit analysis using Kirchhoff’s junction law:
and Kirchhoff’s loop law:
•
Power delivered by emf:
dissipated by resistor:
•
Combinations of resistors:
•
RC circuits: exponential (dis)charging of capacitor thru’ resistor,
;