Formula Sheet - Web Physics
Formula Sheet - Web Physics
Formula Sheet - Web Physics
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Ohm’s Law<br />
r r<br />
E = ρJ<br />
V = IR<br />
Resistivity and Resistance<br />
dL<br />
R = ∫ ρ A<br />
ρ = ρ 1 + α T −T<br />
[ ( )]<br />
0 0<br />
Uniform Currents only<br />
V<br />
E =<br />
L<br />
L<br />
R = ρ<br />
A<br />
I<br />
J =<br />
A<br />
Electric Power<br />
P = IV<br />
2<br />
P = I R<br />
P =<br />
V 2<br />
R<br />
Real Batteries<br />
V = E − Ir<br />
Addition of Resistors<br />
RT<br />
= R1 + R2<br />
+ ... series<br />
1 1 1<br />
= + + ... parallel<br />
R R R<br />
T<br />
1 2<br />
Kirchoff’s rules<br />
V = 0<br />
∑<br />
∑<br />
loop<br />
node<br />
I = 0<br />
RC circuits (charging)<br />
t<br />
−<br />
τ<br />
I = Ie<br />
i<br />
⎛<br />
Q= Qf<br />
⎜1<br />
−e<br />
⎝<br />
t<br />
−<br />
τ<br />
⎞<br />
⎟<br />
⎠<br />
<strong>Formula</strong> <strong>Sheet</strong> for <strong>Physics</strong> 251<br />
RC circuits (discharging) Ampere’s Law<br />
t<br />
r r<br />
−<br />
τ<br />
I = Ie<br />
∫ B⋅ dl = µ<br />
0<br />
Ienc<br />
+ I<br />
i<br />
t<br />
where<br />
−<br />
τ<br />
Q=<br />
Qe<br />
i<br />
dϕ<br />
E<br />
Id<br />
= ε0<br />
τ = RC<br />
dt<br />
Magnetic Force and<br />
Torque<br />
r r r<br />
F = qv × B<br />
r r r<br />
dF = Idl × B<br />
r r<br />
τ = µ × B<br />
r r<br />
U =−µ<br />
⋅B<br />
Cyclotron Motion<br />
R =<br />
mv<br />
qB<br />
2πm<br />
T =<br />
qB<br />
qB<br />
ωc<br />
=<br />
m<br />
Flux and Gauss’s Law for<br />
Magnetism<br />
r<br />
ϕ = B⋅da<br />
∫∫ r<br />
ϕclosed = 0<br />
Sources of Magnetic<br />
Fields<br />
r<br />
µ qv × rˆ<br />
0<br />
B =<br />
2<br />
4π<br />
r<br />
r<br />
r µ Idl × rˆ<br />
0<br />
B = ∫<br />
2<br />
4π<br />
r<br />
µ<br />
0I<br />
B = ∞straight wire<br />
2πr<br />
µ<br />
0I<br />
B = center of loop<br />
2R<br />
B = µ<br />
0nI∞solenoid<br />
µ<br />
0NI<br />
toroidal<br />
B =<br />
2πr<br />
solenoid<br />
τ = RC<br />
* indicates formulas that are specific to ideal gases<br />
† indicates formulas that are specific to parallel-plate capacitors<br />
Faraday’s Law<br />
( )<br />
dϕ<br />
B<br />
E =−<br />
dt<br />
or<br />
r r r r<br />
E⋅ dl = B⋅da<br />
∫<br />
C<br />
∫∫<br />
Mutual Inducance<br />
M<br />
N 1ϕB1<br />
N ϕ<br />
= =<br />
I2<br />
I1<br />
=−M dI 2<br />
E1<br />
dt<br />
=−M dI 1<br />
E2<br />
dt<br />
Self Inductance<br />
Nϕ<br />
B<br />
L =<br />
I<br />
E =−L dI<br />
dt<br />
1 2<br />
U = LI<br />
2<br />
S<br />
d<br />
2 B2<br />
RL Circuits (charging)<br />
⎛<br />
I = If<br />
⎜1<br />
−e<br />
⎝<br />
VL<br />
= Ve<br />
0<br />
L<br />
τ =<br />
R<br />
t<br />
−<br />
τ<br />
t<br />
−<br />
τ<br />
⎞<br />
⎟<br />
⎠<br />
RL Circuits (discharging)<br />
I = Ie<br />
VL<br />
= Ve<br />
i<br />
L<br />
τ =<br />
R<br />
i<br />
t<br />
−<br />
τ<br />
t<br />
−<br />
τ<br />
AC Circuits (general)<br />
XL<br />
= ωL<br />
1<br />
XC<br />
=<br />
ωC<br />
2 2<br />
Z = R + ( XL<br />
− XC)<br />
XL<br />
− XC<br />
tanϕ<br />
=<br />
R<br />
I = I0<br />
cosωt<br />
V = V0<br />
cos( ωt<br />
+ ϕ)<br />
V0 = I0Z<br />
V0<br />
Vrms<br />
=<br />
2<br />
I0<br />
Irms<br />
=<br />
2<br />
VR<br />
,max<br />
= IR<br />
VL,max<br />
= IXL<br />
VC,max<br />
= IXC<br />
1 2 1 2<br />
P = I0<br />
R=<br />
I0<br />
Zcosϕ<br />
2 2<br />
AC Circuits (resonance)<br />
ϕ = 0<br />
Z = R<br />
1<br />
ω =<br />
LC<br />
X = X<br />
L<br />
C
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