*Physics Formulas*

*Electricity*

**Here are some formulas related to electricity.**

*Ohm's Law*
Ohm's law gives a relation between the voltage applied a
current flowing

across a solid conductor:

V (Voltage) = I (Current) x R (Resistance)

Power

In case of a closed electrical circuit with applied voltage
V and resistance R, through which current I is flowing,

Power (P) = V2/R = I2R. . . (because V = IR, Ohm's Law)

ALSO READ physics formulas in mechanics

Kirchoff's Voltage Law

For every loop in an electrical circuit:

ΣiVi = 0

where Vi are all the voltages applied across the circuit.

Kirchoff's Current Law

At every node of an electrical circuit:

ΣiIi = 0

where Ii are all the currents flowing towards or away from
the node in the circuit.

ALSO READ Fundamental Physical Constants

Resistance

The physics formulas for equivalent resistance in case of
parallel and series combination are as follows:

Resistances R1, R2, R3 in series:

Req = R1 + R2 + R3

Resistances R1 and R2 in parallel:

Req = R1R2

R1 + R2

For n number of resistors, R1, R2...Rn, the formula will be:

1/Req = 1/R1 + 1/R2 + 1/R3...+ 1/Rn

Capacitors

A capacitor stores electrical energy, when placed in an
electric field. A typical capacitor consists of two conductors separated by a
dielectric or insulating material. Here are the most important formulas related
to capacitors. Unit of capacitance is Farad (F) and its values are generally
specified in mF (micro Farad = 10 -6 F).

Capacitance (C) = Q / V

Energy Stored in a Capacitor (Ecap) = 1/2 CV2 = 1/2 (Q2 / C)
= 1/2 (QV)

Current Flowing Through a Capacitor I = C (dV / dt)

Equivalent capacitance for 'n' capacitors connected in
parallel:

Ceq (Parallel) = C1 + C2 + C3...+ Cn = Σi=1 to n Ci

Equivalent capacitance for 'n' capacitors in series:

1 / Ceq (Series) = 1 / C1 + 1 / C2...+ 1 / Cn = Σi=1 to n (1 / Ci)

Here

C is the capacitance

Q is the charge stored on each conductor in the capacitor

V is the potential difference across the capacitor

Parallel Plate Capacitor Formula:

C = kε0 (A/d)

Where

k = dielectric constant (k = 1 in vacuum)

ε0 =
Permittivity of Free Space (= 8.85 ×
10-12 C2 / Nm2)

A = Plate Area (in square meters)

d = Plate Separation (in meters)

Cylinrical Capacitor Formula:

C = 2π kε0 [L / ln(b / a)]

Where

k = dielectric constant (k = 1 in vacuum)

ε0 =
Permittivity of Free Space (= 8.85 ×
10-12 C2 / Nm2)

L = Capacitor Length

a = Inner conductor radius

b = Outer conductor radius

Spherical Capacitor Formula:

C = 4π kε0 [(ab)/(b-a)]

Where

k = dielectric constant (k = 1 in vacuum)

ε0 =
Permittivity of Free Space (= 8.85 ×
10-12 C2 / Nm2)

a = Inner conductor radius

b = Outer conductor radius

Inductors

An inductor is an electrical component which resists the
flow of electrons or electric current through it. This property of inductance,
in these devices, is caused by the electromotive force,Inductors in a Series
Network created by magnetic field induced in them. The unit of inductance is
Henry. Here are some important formulas associated with inductors.

Energy Stored in Inductor (Estored) = 1/2 (LI2)

Where, L is inductance and I is the current flowing through
the inductor.

Inductance of a cylindrical air core Coil (L) = (m0KN2A / l)

Momentum and Energy Transformations in Relativistic
Mechanics

Consider the same two frames (S, S') as in case of Lorentz
coordinate transformations above. S' is moving at a velocity 'v' along the
x-axis. Here again γis the
Lorentz factor. In S frame (Px, Py, Pz) and in S' frame (Px', Py', Pz') are
momentum components. Now we consider formulas for momentum and energy
transformations for a particle, between these two reference frames in
relativistic regime.

Component wise Momentum Transformations and Energy
Transformations

Px = γ(Px' + vE' /
c2)

Py = Py'

Pz = Pz'

E = γ(E' + vPx)

and

Px' = γ(Px - vE' /
c2)

Py' = Py

Pz' = Pz

E' = γ(E - vPx)

Physical Formulas for Quantities in Relativistic Dynamics

All the known quantities in classical mechanics get
modified, when we switch over to relativistic mechanics which is based on the
special theory of relativity. Here are formulas of quantities in relativistic
dynamics.

Relativistic momentum p = γm0v

where,

m0 is the rest mass of the particle.

Rest mass energy E = m0c2

Total Energy (Relativistic) E = √(p2c2 + m02c4))

Momentum and Energy Transformations in Relativistic
Mechanics

Consider the same two frames (S, S') as in case of Lorentz
coordinate transformations above. S' is moving at a velocity 'v' along the
x-axis. Here again γis the
Lorentz factor. In S frame (Px, Py, Pz) and in S' frame (Px', Py', Pz') are
momentum components. Now we consider formulas for momentum and energy
transformations for a particle, between these two reference frames in
relativistic regime.

Component wise Momentum Transformations and Energy
Transformations

Px = γ(Px' + vE' /
c2)

Py = Py'

Pz = Pz'

E = γ(E' + vPx)

and

Px' = γ(Px - vE' /
c2)

Py' = Py

Pz' = Pz

E' = γ(E - vPx)

Physical Formulas for Quantities in Relativistic Dynamics

All the known quantities in classical mechanics get
modified, when we switch over to relativistic mechanics which is based on the
special theory of relativity. Here are formulas of quantities in relativistic
dynamics.

Relativistic momentum p = γm0v

where

m0 is the rest mass of the particle.

Rest mass energy E = m0c2

Total Energy (Relativistic) E = √(p2c2 + m02c4))

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