Physics 331 Test 3 Formula Sheet
Capacitors and Capacitance
Q
C=
[F] (Farads)
V
Capacitors in Series:
1
1
1
1



 .....
C T C1 C 2 C 3
Capacitors in Parallel:
C T  C1  C 2  C 3  .....
Charging a Capacitor:
t
i(t) 
E - RC
e
R
v R ( t)  E e
-
t
RC
v C ( t)  E(1 - e
-
t
RC
 = RC
)
Discharging a Capacitor:
t
i(t)  
Vo -  
e
R
v R ( t)   Vo e
-
t
-
t
v C ( t)  Vo e  

' = RTC
Energy Stored in a Capacitor
W=
Q2 1
1
 C V2  Q V
2C 2
2
Inductors and Inductance
di
VL = L
dt
Inductors in Series:
LT = L1 + L2 + L3 +. . . .
Inductor in Parallel:
1
1
1
1



 .....
L T L1 L 2 L 3
Current build up (switch initially closed after having been opened)
At v L ( t)  E e
-
t


t
v R ( t)  E(1 - e )

i(t) 
E
R
(1  e
-
t

)
=
Current decay (switch moved to a new position)
-
t
i(t)  I o e  
vR(t) = R i(t)
vL(t) =  RT i(t)
Energy Stored in an Inductor
W=
1 2
LI
2
' =
L
RT
L
R
=2f
f = 1/T
Complex Numbers:
M  a 2  b2
polar form:
Alternating Current
C = M cos  + j M sin 
C = a + j b:
b
  tan -1  
a
C=M
Inductive Reactance:
Resistance
|XL| =  L
R
Impedance:
ZR = R 0
Inductance:
ZC = XC -90 = 1 / (C) -90
Resistance:
Capacitance:
Capacitve Reactance:
Ohm’s Law for AC:
V=IZ
Components in Series:
ZT = Z1 + Z2 + Z3 + . . .
|XC| = 1 / ( C)
ZL = XL 90 =  L 90
Time Domain:
v(t) = Vm sin ( t  )
Phasor Notation:
V = Vrms  
(books notation)
I = Irms  
V = Vm  
(also acceptable)
I = Im  
Vrms = Vm/2
i(t) = Im sin ( t  )
Irms = Im/2
Ohm’s Law V = I R
Power dissipated in a resistor in the form of heat
P=VI=I2R=V2/R
Resistors in Series RT = R1 + R2 + R3 + . . .
Kirchhoff’s Voltage Law: The sum of the voltage drops around any closed loop equals the sum of
the voltage rises around that loop.
Vrise 
Vdrop (around any closed loop)


Rx
RT
Voltage Divider Law:
Vx  V
Resistors in Parallel:
1
1
1
1



 ...
R T R1 R 2 R 3
Kirchhoff’s Current Law: The sum of all current entering a junction, or any portion of a circuit,
equals the sum of the current leaving the same.
 Ienter   Iexit (any junction)
Current Divider Rule: I x  I
RT
Rx