Physics PART - 3

PHYSICS - PART - 3

Nicola Tesla (1856 - 1943 )was a key figure in the development of alternating current electricity,high-voltage transformers, and the transport of electrical power using AC transmission lines. Tesla's viewpoint was not in agreement with the idea of Edison , who committed himself to the use of direct current in power transmission .

 Tesla's approach won out !

Formulas : Alternative Current

1 - Instantaneous value of current → I = I₀ Sin ⍵t  = I₀ Sin(2πvt)    ( I is the instantaneous value of alternating current at an instant I and I₀ is its Peak value . ⍵ is the angular frequency , v is the frequency.)

2 - Instantaneous value of voltage → ɛ = ɛ₀ Sin ⍵t  = ɛ₀ Sin (2πvt)   ( ɛ is the instantaneous value of alternating voltage at instant t and ɛ₀ is its Peak value .)

3 - Root mean square value → ɛᵣₘₛ → ɛ₀ / √2   and  Iᵣₘₛ = I₀ / √2       (ɛᵣₘₛ and Iᵣₘₛ stand for the rms , virtual , effective values of ac voltage and current respectively .)

4 - Average OR Mean values → ɛₘ = 2ɛ₀ / π   and   Iₘ = 2I₀ / π       ( ɛₘ  and Iₘ  are the average OR mean values of ac voltage and current for half cycle respectively .)

5 - Inductive reactance  →  𝒳ⳑ = ⍵L = 2πvL       ( 𝒳ⳑ is the inductive reactance of an inductance L in an ac circuit of frequency v , In an ac circuit , containing inductance , current lags behind the voltage .by π / 2.)

6 - Capacitive reactance → 𝒳𝑐 = 1/⍵C  = 1 / 2πvC   ( 𝒳𝑐 is the capasitive reactance of a capacitance C in an ac circuit , containing inductance , current leads the voltage by π / 2 .)

7 - Impedance of series LCR circuit → Z = √ R² +  (𝒳ⳑ - 𝒳𝑐 )²   = √ R² + ( ⍵L - 1/⍵C )²     (Z is the impedance of series LCR circuit . Resistance R .)

8 - Phase angle  → tan ɸ = ( 𝒳ⳑ - 𝒳𝑐 )/ R  = (⍵L - 1 / ⍵C ) / R     ( ɸ is the phase angle between current and voltage . The sign of ɸ can be positive or negative depending upon whether 𝒳ⳑ is greater or less than 𝒳𝑐 .The phase angle is zero when 𝒳ⳑ = 𝒳𝑐 .)

9 - Net potential difference series LCR circuit → ɛ₀ = √ V²ʀ +  (Vⳑ - V𝑐)²   ( ɛ₀ is the net potential difference across series LCR circuit and Vʀ , Vⳑ and V𝑐 are the pds across R , L and C respectively.)

10 - Average power → Pₐᵥ = ɛᵣₘₛ Iᵣₘₛ cosɸ = I²ᵣₘₛ R    ( Pₐᵥ is the average power delivered by the generator in an LCR circuit . The term cosɸ is called the power factor.)

Pₐᵥ = ɛᵣₘₛ Iᵣₘₛ    ( In case of an Ideal inductor or a capacitor , ɸ is numerically equal to π / 2 and as such P = 0 . Thus , there is no power loss in ideal inductor or a capacitor .)

11 - Resonance frequency → vᵣ = 1 / 2π√LC    ( vᵣ is the resonance frequency of a LCR circuit.)

12 - Quality factor → Q = ⍵ᵣL /R  = 1 / ⍵ᵣCR  = 1/R √L/C    (Q is called the quality factor of an LCR circuit .)

13 - Band Width  → Q = ⍵ᵣ / 2Δ⍵    ( Δ⍵ = R / 2L  is called the band width of the circuit .)

14 - In case of ideal transformer → ɛₚ Iₚ = ɛₛ Iₛ
ɛₛ / ɛₚ = Iₚ / Iₛ = Nₛ / Nₚ
Rₛ / Rₚ = ( Nₛ / Nₚ )²            ( p and s stand for primary and secondary of the transformer respectively.)

Formulas : Electromagnetic Waves

Understanding about the production , propagation and absorption ,of electromagnetic waves has opened the door to modern methods of communication.

The major asymmetry arise due to the fact that there are no "magnetic monopoles " corresponding to "electric charges ". Dissatisfaction with such broken symmetries in nature has often led physicists to important discoveries and to profound insights into the nature of universe.We can see why physicists have not given up the search for magnetic monopoles.

1 - Displacement current → Iɗ = ∊₀ dɸₑ / dt = ∊₀ A dE/ dt = C dV/ dt    ( Iɗ is displacement current . dɸₑ / dt is the rate of change of electric flux , dE / dt is the rate of change of electric field and dV / dt is the rate of change of potential difference .)

2 - The sinusoidally varying electric and magnetic fields → E𝗒 = E₀ Sin ( kx - ⍵t )

B𝗓 = B₀ Sin ( kx - ⍵t )    ( E and B are the plane electromagnetic wave propagating along X - axis. E₀ and B₀ are the maximum values of E and B .

 k (propagation constant ) = 2π /λ

⍵ ( angular frequency ) = 2πv

3 - Speed of Electromagnetic wave in vacuum  → c = 1 /√∊₀𝜇₀ 

speed of electromagnetic wave in medium → v = 1 / √∊𝜇

4 - Instantaneous electric field energy density → uᴇ = 1/2 ∊₀ E²

Instantaneous magnetic field energy density → uʙ = B² / 2𝜇₀       (uᴇ = uʙ , E is the Electric field , B is magnetic field . ∊₀ and 𝜇₀ is electric and magnetic permittivity in vaccum.

5 - Total average energy density → uₐᵥ = 1/2 ∊₀E₀² = B²/2𝜇₀ = 1/2 (E₀B₀ / 𝜇₀c ) = (Eᵣₘₛ Bᵣₘₛ) / 𝜇₀c    ( total average density associated with electromagnetic wave. )

6 - Intensity of electromagnetic wave → I = uₐᵥc = 1/2 c ∊₀ E² = E₀² / 2𝜇₀c = cB₀²/ 2 𝜇₀ = 1/2 (E₀ B₀/  𝜇₀)  = Eᵣₘₛ Bᵣₘₛ / 𝜇₀
I = power/area = (energy/time) / area =( U /t ) / A = U / At   (U is the energy carried by the wave.)

The history of science is filled with many unforeseen surprises . nobody seriously would have expected young Michael Faraday to be anything but an errand boy or book binder , even if he managed to escape an early death from starvation or illness. 

The idea that he might be a scientist or educator was ridiculous and to predict that he would produce the most fundamental changes in the basic theories of Physics, to follow those oh Sir Issac Newton, would have been sheer madness .

Michael Faraday received no formal training in science and mathematics and showed no signs of genius or ability during his very limited formal education . He was the first to use the consept of a field and to picture field lines , which he referred to as "line of force".This approach was to flourish in the hand of James Maxwell , who possessed the mathematical education that Faraday lacked. 

Maxwell read Faraday's work  , as well as the more mathematical work of others . His synthesis resulted in the unification of electricity and magnetism , using the first field theory . Field theory has been an important part of theoretical physics ever since.


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