dX RC dt - physics.purdue.edu

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1 9/30/15 1 RC Circuits RC Circuits 9/30/15 2 Charging a capacitor: C initially uncharged; connect switch to a at t=0 Calculate current and charge as function of time. Apply Kirchhoff’s Voltage Law: ε q C IR = 0 Short term: Long term: ε 0 I 0 R = 0 I 0 = ε R (q = q 0 = 0) ε q C 0 R = 0 q = Cε (I c = 0) Intermediate term: ε q C dq dt R = 0 9/30/15 3 Solution dq dt = ε R q RC dq ε / R q / RC 0 Q = dt 0 t X = ε / R q / RC dX = 1 RC dq RC dX X ε R ε R Q RC = dt 0 t ln x ε R ε R Q RC = ln ε R Q RC ε R = t RC e t RC = 1 Q ε C 9/30/15 4 Continued τ = RC Q = Cε (1 e t /τ ) Capacitive Time Constant: The greater the , the greater the charging time. V c = Q C = ε (1 e t /τ ) I = dQ dt = ε R e t /τ Units of : F = V A C V = C C/s = s
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Transcript of dX RC dt - physics.purdue.edu

ljpnF15_12post.pptC initially uncharged; connect switch to a at t=0
Calculate current and charge as function of time.
• Apply Kirchhoff’s Voltage Law: ε − q C − IR = 0
• Short term:
• Long term:
(Ic = 0)
Intermediate term:
9/30/15 3
Q
dq
ε R − Q RC
Capacitive Time Constant: "
Vc = Q C
Units of :
= C C/s
I = ε R e− t /τ
t = 0 t = ∞ t = τ
t = 0 t = ∞ t = τ
at
at
9/30/15 7
RC Circuits • Discharging a capacitor: • C initially charged with Q=C" • Connect switch S2 at t=0.
• Apply Kirchhoff’s Voltage Law: q C + IR = 0
• Short term:
• Long term:
I0 = −ε R
9/30/15 8

at
at
Behavior of Capacitors
• Charging – Initially, the capacitor behaves like a wire. – After a long time, the capacitor behaves like an open
switch in terms of current flow.
• Discharging – Initially, the capacitor behaves like a variable battery. – After a long time, the capacitor behaves like an open
switch
9/30/15 12
Magnetic Field
• Large Magnetic fields are used in MRI (Nobel prize for medicine in 2003)
• Extremely Large magnetic field are found in some stars
• Earth has a Magnetic Field
4
N
S
N
S
Attraction
S
N
N
S
Repulsion
• Bar magnet ... two poles: N and S Like poles repel; Unlike poles
attract. • Magnetic Field lines: (defined in
same way as electric field lines, direction and density)
NS
DEMO
Magnetic Field Lines of a bar magnet
Electric Field Lines of an Electric Dipole
NS
N S N N S S
• In fact no attempt yet has been successful in finding magnetic monopoles in nature but scientists are looking for them.
• One explanation: there exists magnetic charge, just like electric charge. An entity which carried this magnetic charge would be called a magnetic monopole (having + or - magnetic charge).
9/30/15 16
Earth’s Magnetic Field
Since 1904: 750 km, an average of 9.4 km per year.
From 1973 to late 1983: 120 km, an average of 11.6 km per year
Earth’s Magnetic Field