## 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 I^{2}

## 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:

- Instantaneous power = V
_{m}I_{m}cos(ωt) = V_{m}I_{m}cos ϕ - Average power = (1/2) Vm Im cos ϕ
- Apparent power = V
_{rms}I_{rms} - 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:

- {N_1 \over N_2} = {V_1 \over V_2}
- {E_1 / E_2} = {N_1 / N_2} = {V_1 / V_2}
- Turns ratio = {N_1\over N_2} = {V_1\over V_2} = {I_2\over I_1}
- Efficiency = {Output Power \over Input Power} × 100%

Where

- E
_{1}and E_{2}are the primary and secondary emf respectively, - N
_{1}and N_{2}are the number of turns in the primary and secondary coils, and - V
_{1}and V_{2}are the primary and secondary voltages.

**AC Generator:**

Maximum EMF induced = NBAω sin(ωt)

RMS EMF induced = (NBAω)/√2