Electromagnetic Induction and Alternating Current Formula

Faraday’s Law of Electromagnetic Induction:

EMF induced (ε) = – N dΦ\over dt

• ε is the induced electromotive force,
• N is the number of turns in the coil,
• (dΦ/dt) is the rate of change of magnetic flux through the coil

Lenz’s Law: The direction of the induced current is such that it opposes the change causing it.

Self-Inductance:

EMF induced (ε) = -LdI\over dt or L = – ε/dI\over dt

• ε is the induced electromotive force,
• L is the self-inductance of the coil,
• (dI/dt) is the rate of change of current in the coil

Mutual Inductance:

EMF induced (ε) = -MdI\over dt or M = – ε/dI\over dt

• ε is the induced electromotive force,
• M is the mutual inductance between two coils, and
• (dI/dt) is the rate of change of current in the primary coil.

Energy Stored in an Inductor:

Energy stored = (1/2) L I²

Alternating Current (AC) Voltage and Current:

Instantaneous voltage = V_m sin(ωt)

Instantaneous current = I_m sin(ωt + ϕ)

• Peak voltage = V_m
• Peak current = I_m
• Angular frequency = ω = 2πf
• Phase difference = ϕ

Root Mean Square (RMS) Values:

V_rms = V_m/√2

I_rms = I_m/√2

Where

• V_rms is the root mean square value of voltage,
• V_m is the maximum voltage,
• I_rms is the root mean square value of the current,
• I_m is the maximum current.

Power in AC Circuit:

1. Instantaneous power = V_m I_m cos(ωt) = V_m I_m cos ϕ
2. Average power = (1/2) Vm Im cos ϕ
3. Apparent power = V_rms I_rms
4. Power factor = cos ϕ = Real\ power\over Apparent\ power

9. LC Oscillations:
– Angular frequency = ω = 1/√(LC)
– Time period = T = 2π/ω

Resonance Frequency (f):

f = 1\over (2π \sqrt{LC})

Where

• f is the resonance frequency,
• L is the inductance, and
• C is the capacitance in the LC circuit.

Quality Factor (Q):

Q = {1\over R} \sqrt{L\over C}

Where

• Q is the quality factor,
• R is the resistance,
• L is the inductance, and
• C is the capacitance in the LC circuit.

Transformers:

1. {N_1 \over N_2} = {V_1 \over V_2}
2. {E_1 / E_2} = {N_1 / N_2} = {V_1 / V_2}
3. Turns ratio = {N_1\over N_2} = {V_1\over V_2} = {I_2\over I_1}
4. Efficiency = {Output Power \over Input Power} × 100%

Where

• E₁ and E₂ are the primary and secondary emf respectively,
• N₁ and N₂ are the number of turns in the primary and secondary coils, and
• V₁ and V₂ are the primary and secondary voltages.

AC Generator:

Maximum EMF induced = NBAω sin(ωt)

RMS EMF induced = (NBAω)/√2