Alternating Current — Complete Formula

Basic AC Quantities

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Instantaneous Current	[i = I_0 \sin(\omega t)]	[I_0] = peak current, [\omega] = angular frequency	A	AC varies sinusoidally ⭐
Instantaneous Voltage	[v = V_0 \sin(\omega t)]	[V_0] = peak voltage	V	Same frequency
Angular Frequency	[\omega = 2\pi f]	[f] = frequency	rad/s	Basic relation ⭐
Time Period	[T = \dfrac{1}{f}]	—	s	Cycle time

💡 Memory Hint:
AC → sinusoidal variation

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
RMS Current	[I_{rms} = \dfrac{I_0}{\sqrt{2}}]	—	A	Effective value ⭐
RMS Voltage	[V_{rms} = \dfrac{V_0}{\sqrt{2}}]	—	V	Used in circuits ⭐
Average Current	[I_{avg} = \dfrac{2I_0}{\pi}]	—	A	Over half cycle ⚠️

💡 Memory Hint:
RMS = 0.707 × peak value

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Ohm’s Law	[V = IR]	—	—	Same as DC ⭐
Phase Relation	Voltage in phase with current	—	—	No phase difference ⭐
Power	[P = V_{rms} I_{rms}]	—	W	All power consumed ⭐

💡 Memory Hint:
Resistor → no phase difference

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Inductive Reactance	[X_L = \omega L]	[L] = inductance	Ω	Opposes current ⭐
Current	[I = \dfrac{V}{X_L}]	—	A	Decreases with frequency
Phase Relation	Current lags by [\dfrac{\pi}{2}]	—	—	Important ⭐

💡 Memory Hint:
Inductor → current lags voltage

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Capacitive Reactance	[X_C = \dfrac{1}{\omega C}]	[C] = capacitance	Ω	Opposes voltage ⭐
Current	[I = \dfrac{V}{X_C}]	—	A	Increases with frequency
Phase Relation	Current leads by [\dfrac{\pi}{2}]	—	—	Important ⭐

💡 Memory Hint:
Capacitor → current leads voltage

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Impedance	[Z = \sqrt{R^2 + (X_L – X_C)^2}]	[Z] = impedance	Ω	Total opposition ⭐
Current	[I = \dfrac{V}{Z}]	—	A	AC version of Ohm’s law
Phase Angle	[\tan\phi = \dfrac{X_L – X_C}{R}]	[\phi] = phase angle	—	Determines lead/lag ⭐

💡 Memory Hint:
Impedance = AC resistance

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Power	[P = V_{rms} I_{rms} \cos\phi]	[\phi] = phase angle	W	Real power ⭐
Power Factor	[\cos\phi = \dfrac{R}{Z}]	—	—	Efficiency measure ⭐

💡 Memory Hint:
Power factor → how effectively power is used

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Resonance Condition	[X_L = X_C]	—	—	Inductive = capacitive ⭐
Resonant Frequency	[f = \dfrac{1}{2\pi\sqrt{LC}}]	—	Hz	Very important ⭐
Impedance at Resonance	[Z = R]	—	Ω	Minimum impedance ⭐
Current	Maximum	—	—	Peak current ⭐

💡 Memory Hint:
Resonance → maximum current

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Voltage Ratio	[\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p}]	[N] = turns	—	Step-up/down ⭐
Current Ratio	[\dfrac{I_s}{I_p} = \dfrac{N_p}{N_s}]	—	—	Inverse relation
Power	[V_p I_p = V_s I_s]	—	W	Ideal transformer ⭐

💡 Memory Hint:
Voltage ↑ → current ↓ (energy conserved)

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