Download Physics 2102 Spring 2002 Lecture 8

Physics 2113
Jonathan Dowling
Lecture 24: FRI 13 MAR
DC circuits III
Ch27.4-9
One Battery? Simplify!
Resistors
Key formula: V=iR
In series: same current dQ/dt
Req=∑Rj
In parallel: same voltage
1/Req= ∑1/Rj
P = iV = i2R = V2/R
Capacitors
Q=CV
same charge Q
1/Ceq= ∑1/Cj
same voltage
Ceq=∑Cj
U = QV/2 = Q2/2C = CV2
Many Batteries? Loop & Junction!
One Battery: Simplify First
Three Batteries: Straight to
Loop & Junction
RC Circuits: Charging a Capacitor
In these circuits, current will change for a while, and then stay constant.
We want to solve for current as a function of time i(t)=dq/dt.
The charge on the capacitor will also be a function of time: q(t).
The voltage across the resistor and the capacitor also change with time.
To charge the capacitor, close the switch on a.
E + VR (t) + VC (t) = 0
VC=Q/C
VR=iR
E - i(t)R - q(t) /C = 0
E - ( dq /dt ) R - q(t) /C = 0
A differential equation for q(t)! The solution is:
Time constant:  = RC
q(t) = CE (1- e-t / RC )
Time i drops to 1/e.
-t / RC
® i(t) º dq /dt = (E /R)e
i(t)
E/R
CE
t
t
RC Circuits: Discharging a Capacitor
Assume the switch has been closed
on a for a long time: the capacitor will
be charged with Q=CE.
+++
---
Then, close the switch on b: charges find their way across the circuit,
establishing a current.
V +V = 0
R
C
-i(t)R + q(t) /C = 0 ® ( dq /dt ) R + q(t) /C = 0
+
-C
-t / RC
-t / RC
q(t)
=
q(0)e
=
CEe
Solution:
i(t) = dq /dt = (q(0) /RC)e-t / RC = (E /R)e-t / RC
i(t)
E/R
t
t
1
1
1
=
+ ® R23par = 12W
par
R23
R2 R3
Too Many Batteries!
• Fire Hazard: Filling gas can in pickup truck with plastic bed liner.
• Safe Practice: Always place gas can on ground before refueling.
• Touch can with gas dispenser nozzle before removing can lid.
• Keep gas dispenser nozzle in contact with can inlet when filling.