Class 12 Physics Chapter 7 Alternating Current

This Alternating Current Class 12 Notes PDF is made exactly for moments when the chapter feels overwhelming and time is short. The notes focus on NCERT-aligned concepts, so you don’t feel lost in derivations or messy graphs. 

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You can revise directly on your phone, re-read key ideas just before the exam, or use it for last-minute panic preparation without opening multiple books. Every important concept is explained in a simple, board-friendly way, with emphasis on why things happen

What is Alternating Current?

Alternating Current (AC) is an electric current whose magnitude and direction change periodically with time.

Mathematical representation ⇒ i(t) = I₀ sin(ωt) and  v(t) = V₀ sin(ωt), where

• I₀ = Peak current
• V₀ = Peak voltage
• ω = Angular frequency = 2πf
• f = Frequency

AC is preferred over DC because it can be stepped up or down using transformers, making long-distance transmission efficient.

Average Value of AC

For a complete cycle ⇒ Average value of AC = 0 (because positive and negative halves cancel each other)

So instead, we calculate average over half cycle I_avg = 2I₀/π

However, average value is not practically useful. Therefore, RMS value is used.

RMS Value of Alternating Current

RMS (Root Mean Square) value of AC is the effective value of current or voltage that produces the same heating effect as DC.

I_rms = I₀/√2 and V_rms = V₀/√2

So for example, if household supply is 220 V, it means 220 V (RMS).

Relation between peak and RMS ⇒ L₀ = √2 L_rms and V₀ = √2 V_rms

AC Through a Pure Resistor

In a resistor:

• Voltage and current are in phase
• Both reach maximum and zero at the same time

Graphically:

• Peaks coincide
• No phase difference

Power ⇒ P = VI

Power is always positive → energy is continuously consumed as heat.

Derivation:

Applied voltage ⇒ v = V₀sin(ωt)

Current ⇒ i = (V₀/R) sin(ωt)

Since ⇒ I₀ = V₀ / R

Phase relation ⇒ Voltage and current are in phase (φ = 0)

Average power consumed ⇒ P_avg = V_rms L_rms

Since cosφ = 1 for resistor ⇒ P_avg = V_rms L_rms cosφ

Power is always positive → energy is continuously dissipated as heat.

AC Through a Pure Inductor

An inductor resists change in current by storing energy in its magnetic field. So, current lags behind voltage by 90°

Inductive reactance ⇒ X_L = ωL

Points to Remember:

• Higher frequency → higher opposition
• No power loss (ideal inductor)

Derivation:

Voltage-current relation ⇒ V = L (di/ dt)

Current ⇒ i = I₀ sin(ωt − π/2)

Phase relation ⇒ Current lags voltage by 90° (π/2)

Inductive reactance ⇒ X_L = ωL

Current amplitude ⇒ I₀ = V₀ / X_L

Average power ⇒ P_avg = V_rms L_rms cos90° ⇒ P_avg = 0

Thus, no average power is consumed. This is called wattless current.

AC Through a Pure Capacitor

A capacitor stores charge and releases it quickly. So, current leads voltage by 90°

Capacitive reactance ⇒ X_C = 1/ωC

Important points:

• Higher frequency → less opposition
• No power loss (ideal capacitor)

Derivation:

Current-voltage relation ⇒ i = C (dV/ dt)

Current ⇒ i = I₀ sin(ωt + π/2)

Phase relation ⇒ Current leads voltage by 90° (π/2)

Capacitive reactance ⇒ X_C = 1 / (ωC)

Current amplitude ⇒ I₀ = V₀ / X_C

Average power ⇒ P_avg = V_rms L_rms cos90° = 0

Thus, the capacitor also consumes no average power (wattless current).

LCR Series Circuit

When R, L, and C are connected in series, opposition to AC is called impedance (Z).

Phase difference ⇒ Z = √(R² + (X_L – X_C)²

Current ⇒ I₀ = V₀ / Z

Phase angle ⇒ tan Φ = (X_L – X_C)/R

• If X_L > X_C: current lags
• If X_C > X_L: current leads

Resonance in LCR Circuit (Very Important)

Resonance occurs when ⇒ X_L = X_C

ω₀ L = 1 / (ω₀C)

Resonant angular frequency ⇒ ω₀ = 1 / √(LC)

Resonant frequency ⇒ f₀ = 1 / (2π√LC)

At resonance:

• Impedance Z = R (minimum)
• Current is maximum
• Power factor = 1
• Circuit behaves like pure resistor

Used in:

• Radio tuning
• TV receivers
• Communication systems

Power in AC Circuits - Very Important

Instantaneous power ⇒ P = v i

Average power ⇒ P_avg = V_rms L_rms cosφ, where cosφ is called power factor.

Power factor ⇒ cosφ = R / Z

Cases:

• Pure resistor → cosφ = 1 → maximum power
• Pure inductor/capacitor → cosφ = 0 → zero average power

Industries use capacitors to improve power factor.

LC Oscillations

In an LC circuit, energy oscillates between the electric field of the capacitor, and the magnetic field of the inductor. Total energy remains constant in an ideal LC circuit.

Quality Factor (Q-Factor)

Quality factor of LCR circuit ⇒ Q = ω₀L / R; It measures sharpness of resonance.

• Higher Q → sharper resonance
• Lower Q → broader resonance

Transformer - Application of AC

A transformer works only on AC. Principle ⇒ Mutual induction

Turns ratio ⇒ V_s/V_p = N_s/N_p, where V_s = Secondary voltage; V_p = Primary voltage; N_s = Secondary turns; and N_p = Primary turns

• For ideal transformer ⇒ V_p L_p = V_s L_s
• Step-up transformer ⇒ N_s > N_p → increases voltage
• Step-down transformer ⇒ N_s < N_p → decreases voltage

Used in:

• Power transmission
• Chargers
• Adapters

FAQs

1. What is alternating current in Class 12 Physics?

Ans. Alternating current (AC) is an electric current whose magnitude and direction change periodically with time. It is represented as ⇒  i = I₀ sin(ωt)

2. What is the formula for the RMS value of AC?

Ans. The RMS value of current and voltage is ⇒ I_rms = I₀/√2 and V_rms = V₀/√2. RMS value represents the effective value of AC equivalent to DC in terms of heating effect.

3. Why is the average value of AC zero?

Ans. The average value of AC over one complete cycle is zero because the positive and negative halves of the sine wave cancel each other.

4. What is impedance in an LCR circuit?

Ans. Impedance (Z) is the total opposition offered to AC in a circuit containing resistance, inductance, and capacitance. Z = √[R² + (X_L − X_C)²]. It combines resistance and reactance.

5. What is the resonance condition in an LCR circuit?

Ans. Resonance occurs when ⇒ X_L = X_C; Resonant frequency ⇒ f₀ = 1 / (2π√LC)/ At resonance, impedance is minimum, current is maximum, and power factor is 1.

6. What is the power factor in AC circuits?

Ans. Power factor is defined as ⇒ cosφ = R / Z. It indicates how effectively electrical power is being converted into useful work. For a pure resistor, power factor = 1. For a pure inductor or capacitor, power factor = 0.

7. Why is power zero in a pure inductor or capacitor?

Ans. In a pure inductor or capacitor, the phase difference between voltage and current is 90°. Since: P_avg = V_rms L_rms cos90° ⇒ P_avg = 0. No average power is consumed. This is called wattless current.