Reference Guide & Formula Sheet for Physics - 2006 Version

Reference Guide & Formula Sheet for Physics
Dr. Mitchell A. Hoselton Physics − Douglas C. Giancoli Page 8 of 16
Chapter 17. –
Capacitors and Capacitance
Q c = C•V c
Q c = charge on capacitor
(The unit of electric charge is the coulomb = C)
C = capacitance of the capacitor
(The unit of capacitance is the farad = F = C/V)
V c = voltage across the plates
(The unit of voltage is the volt = V = J/C)
Chapter 19. –
Resistor Combinations
SERIES
R eq = R 1 + R 2 + R 3 +. . .
1
R
eq
=
1
R
1
+
1
R
PARALLEL
2
+ K +
1
R
n
=
n
∑
i=
1
1
R
i
Potential Energy stored in a Capacitor
P = ½•C•V²
Chapter 18. –
Ohm's Law
V = I•R
V = voltage across the resistor
(The unit of voltage is the volt = V = J/C)
I = current through the resistor
(The unit of current is the ampere = A = C/s)
R = resistance of the resistor
(The unit of resistance is the ohm = Ω = V/A)
Resistance of a resistor (or any resistive material)
R = ρ•L / A x
ρ = resistivity of the material
(The unit of resistivity is the ohm•meter = Ω•m)
L = length of the material
(The unit of length is the meter = m)
A x = cross-sectional area of the
Material or resistor
(The unit of cross-sectional area is meter 2 = m 2 )
Electric Power (The unit of power is the watt = W = J/s)
P = I²•R
P = V ² / R
P = I•V
Capacitor Combinations
SERIES
1
=
1
Kirchhoff’s Laws
1
+
C
1
+ K +
C
PARALLEL
C eq = C 1 + C 2 + C 3 + …
Node Rule: Σ node I i = 0
Loop Rule: Σ loop ∆V i = 0
Capacitance, C, of a Capacitor
C = κ•εo•A / d
n 1
= ∑
i =
C
1
C C
eq
1
2
n
κ = dielectric constant
A = area of plates
d = distance between plates
ε o
= 8.85 10 −12 ) F/m
(Capital “C” is also used as the abbreviation for the unit of electric
charge; the coulomb = C. Do not confuse the two uses of capital “C”.
The unit of capacitance is the farad = F. The capital “F” is frequently
used as the symbol for force. Do not confuse the two used of the
capital “F”.)
RC Circuit formula (Charging with one battery, one
resistor and one capacitor)
V Battery
− V capacitor − I•R = 0
RC Circuits (Charging) - R•C = τ = time constant
V c = V MAX •[1 - e −t/RC ]
But V c − I•R = 0 (from Ohm’s Law), therefore,
I = (V MAX /R)•e −t/RC
= I MAX•e −t/RC
And Q c = CV c (from the definition of capacitance), so
Q c = C•V MAX •[1 − e −t/RC ]
= Q MAX •[1 − e −t/RC ]
i
Version 6/5/2006