Science
Equations
R
Radioactive Decay
N
=
N
0
e
-
λt
Range of Projectile
R
=
v
2
sin
2
θ
g
Rectangle, Area of
A
=
x
y
Reactance of a Capacitor
X
c
=
1
ω
C
Reactance of an Inductor
X
L
=
ω
L
Refractive Index
n
=
C
C
matter
n
=
sin
i
sin
r
if
the
other
refractive
index
=
1
Refractive Index Related to Wave Velocities
n
=
c
v
c
m
Regular Polygon, Area of
A
=
n
s
r
2
=
p
r
2
Relativistic Mass
m
=
m
0
1
-
v
2
c
2
Relativistic Mass-Energy Relation
E
=
m
c
2
Resolving Power (Rayleigh criterion)
Δ
l
=
1.22
fλ
D
Resonance Condition for
I
X
L
=
X
C
Resistivity
E
=
ρ
J
ρ
=
R
A
l
Resistor in Parallel
1
R
=
1
R
1
+
1
R
2
+
L
+
1
R
n
Resistor in Series
R
=
R
1
+
R
2
+
L
+
R
n
Rhombus, Area of
A
=
x
1
x
2
2
RMS speed of molecules in ideal gas
c
2
¯
=
(
3
R
T
M
)
1
/
2
=
(
3
p
ρ
)
1
/
2
Root Mean Square Current
I
r
m
s
=
I
0
/
2
Root Mean Square Voltage
V
r
m
s
=
V
0
/
2
Rotational kinetic energy
T
=
1
2
I
ω
2
S
Scale of Temperature
θ
100
=
x
θ
-
x
0
x
100
-
x
0
Secant and Tangent, Intersecting
s
t
=
t
e
t
2
=
se
Secants, Intersecting
se
=
s
′
e
′
Sector, Area of
A
=
n
π
r
2
360
∘
Segment, Area of
A
=
n
π
r
2
360
∘
-
b
h
2
Self-Inductance
L
=
NΦ
I
Serial Relation
λ
1
N
1
=
λ
2
N
2
Serial Relation for n
n
1
sin
θ
1
=
n
2
sin
θ
2
Series Resistance
R
=
R
1
+
R
2
+
.
.
.
Specific Heat Capacity
c
=
H
m
θ
Specific Latent Heat
H
=
ml
Sphere, Surface Area of
S
=
4
πr
2
Sphere, Volume of
V
=
4
π
3
r
3
Spiral Spring, Simple Harmonic Motion
T
=
2
π
m
k
Spring Constant
F
=
k
x
Square, Area of
A
=
x
2
Standard deviation
s
=
1
N
Σ
i
=
1
N
(
x
i
-
x
)
2
Standing Wave
E
=
2
E
0
sin
k
x
cos
ω
t
E
=
2
E
0
sin
(
2
π
x
λ
)
cos
(
2
π
t
T
)
Stefan's Law
P
=
ε
σ
A
(
T
4
-
T
e
4
)
Stellar Parallax
d
=
1
P
Surface Area of a Cube
s
=
6
e
2
Surface Area of a Cuboid
s
=
2
lw
+
2
lh
+
2
wh
Surface Area of a Cylinder
s
=
2
π
r
2
+
2
πrh
=
2
πr
(
r
+
h
)
T
Tangent and Secant, Intersecting
s
t
=
t
e
t
2
=
se
Telescopic Magnification
m
=
f
0
f
e
Temperature Variation of Resistance
R
θ
=
R
0
(
1
+
αθ
)
Thermal Conductivity
k
=
1
3
C
v
,
vol
c
¯
l
Thin Film Interference
d
cos
θ
i
=
(
2
m
+
1
)
λ
f
4
for
maxima
d
cos
θ
i
=
2
m
λ
f
4
for
minima
Thin Prism
d
=
A
(
n
-
1
)
Time of Flight of Projectile
t
=
2
v
sinθ
g
Time period, circular motion
T
=
2
π
ω
Torque on a solenoid
Γ
=
NIAB
sinα
Total Energy, Simple Harmonic Motion
E
=
1
2
m
ω
2
r
2
Transformer
V
2
V
1
=
-
N
2
N
1
Trapezoid, Area of
A
=
h
2
(
x
1
+
x
2
)
Travelling Wave
Ψ
=
a
sin
(
ω
t
-
k
x
)
Ψ
=
a
sin
2
π
(
t
T
-
x
λ
)
y
=
a
sin
2
π
(
t
T
-
x
λ
)
Triangle, Area of
A
=
b
h
2
=
a
b
sin
C
2
Triangle (Equilateral), Area of
A
=
h
2
3
3
=
a
2
3
4
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