Physics 331 Final Exam Formula Sheet
Ohm’s Law
V=IR
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
Voltage Divider Law:
Vx  V
RT
1
1
1
1



 ...
Resistors in Parallel:
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:
Capacitors:
Q
C=
[F] (Farads)
V
Ix  I
RT
Rx
Capacitor 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
Inductors and Inductance
VL = L
di
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

)
=
L
R
Current decay (switch moved to a new position)
-
t
i(t)  I o e  
vR(t) = R i(t)
Alternating Current
f = 1/T
=2f
Complex Numbers:
C=a+jb
M  a 2  b2
polar form:
vL(t) =  RT i(t)
:
' =
L
RT
C = M cos  + j M sin 
b
  tan -1  
a
C=M
Inductive Reactance:
Capacitve Reactance:
Resistance
|XL| =  L
|XC| = 1 / ( C)
R
Impedance:
ZR = R 0
ZL = XL 90 =  L 90
ZC = XC -90 = 1 / (C) -90
Resistance:
Inductance:
Capacitance:
Ohm’s Law for AC:
V=IZ
Time Domain:
v(t) = Vm sin ( t  )
Phasor Notation:
V = Vrms  
(books notation)
I = Irms  
V = Vm  
(also acceptable)
I = Im  
Vrms = Vm/2
Vm = 2 Vrms
Irms = Im/2
Im = 2 Irms
i(t) = Im sin ( t  )
Components in Series
ZT = Z1 + Z2 + Z3 + . .
Z
Voltage Divider Rule:
Vx  VT x
ZT
1
1
1
1



 ...
Components in Parallel:
Z T Z1 Z 2 Z 3
Z
Current Divider Rule:
Ix  IT T
Zx
ZZ
Two impedance values in parallel:
ZT  1 2
Z1  Z 2
In general the equivalent of Ohm’s Law is always satisfied
e
iT 
vR = iR R
vC = iC XC
vL = i L XL
ZT
magnitudes only