Simple Alternating Current (A.C.) Circuits

Alternating Current (A.C.) is an electric current that reverses its direction periodically with time, unlike Direct Current (D.C.) which flows in only one direction. In Physics, understanding A.C. involves studying how resistors, inductors, and capacitors behave when connected to an alternating voltage source.

1. Peak and R.M.S. Values

In an A.C. circuit, the voltage and current vary sinusoidally. The maximum value reached in either direction is the Peak Value (V₀ or I₀). However, the effective value used for calculations is the Root Mean Square (R.M.S.) Value.

• V_rms = V₀ / √2 ≈ 0.707 V₀
• I_rms = I₀ / √2 ≈ 0.707 I₀

Note: Most A.C. measuring instruments (like a.c. ammeters and voltmeters) record R.M.S. values.

2. Components in A.C. Circuits

The behavior of current depends on the component in the circuit:

• Pure Resistor: Current and voltage are in phase (phase angle φ = 0°).
• Pure Inductor: Voltage leads current by 90° (π/2 radians). The opposition is called Inductive Reactance (X_L = 2πfL).
• Pure Capacitor: Current leads voltage by 90° (π/2 radians). The opposition is called Capacitive Reactance (X_C = 1 / 2πfC).

3. Series R-L-C Circuits and Impedance

When a resistor (R), inductor (L), and capacitor (C) are connected in series, the total opposition to current is called Impedance (Z).

The formula for Impedance is: Z = √[R² + (X_L - X_C)²]

The effective voltage (V) is: V = √[V_R² + (V_L - V_C)²]

4. Phase Angle and Power Factor

The phase angle (φ) between the supply voltage and current is given by: tan φ = (X_L - X_C) / R.

Power Factor: This is defined as the ratio of the real power to the apparent power. It is equal to cos φ or R / Z. For a pure resistor, the power factor is 1; for a pure inductor or capacitor, it is 0.

5. Resonance in A.C. Circuits

Resonance occurs in a series R-L-C circuit when the inductive reactance equals the capacitive reactance (X_L = X_C). At this point:

• Impedance is at its minimum (Z = R).
• Current is at its maximum.
• The resonant frequency (f₀) is given by: f₀ = 1 / (2π√LC)