Alternating Current (Copy)

A2 Level Physics – Section 21: Alternating Currents (Detailed Notes)

21.1 Characteristics of Alternating Currents

1. Key Terms

• Period (T): Time for one full cycle of the alternating current/voltage (s)
• Frequency (f): Number of complete cycles per second (Hz), f = 1 / T
• Peak value (x₀): Maximum value reached by the alternating current (I₀) or voltage (V₀)

2. Sinusoidal Equation

• Alternating current or voltage varies sinusoidally:
  • x(t) = x₀·sin(ωt)
  • x = instantaneous current or voltage
  • x₀ = peak value
  • ω = angular frequency = 2πf
  • t = time (s)

Graphically:

• Symmetrical wave oscillating about 0
• Repeats every T seconds
• Crosses zero twice every cycle

3. Power in Resistive Load

• P(t) = I(t)²·R = I₀²·sin²(ωt)·R
• Mean of sin²(ωt) over one cycle = ½

So:

• P_mean = ½·I₀²·R = ½·P_max

4. Root-Mean-Square (r.m.s.) Values

• I_rms = I₀ / √2
• V_rms = V₀ / √2

r.m.s. values:

• Give the equivalent DC values for power calculations
• For resistive loads: P = I_rms²·R = V_rms² / R

Key identities:

• P = I_rms·V_rms
• P = ½·I₀·V₀ (for sinusoidal wave)

21.2 Rectification and Smoothing

1. Rectification Overview

• Rectification: Converting AC to DC
• Half-wave rectification: Only one half (positive or negative) of the AC cycle is used
• Full-wave rectification: Both halves are used (with inversion of negative half)

2. Half-Wave Rectification (Single Diode)

• Diode allows current in one direction only:
  • During positive half-cycle: diode conducts, output follows input
  • During negative half-cycle: diode blocks, output = 0

Graph:

• One sine peak every 2π
• Flatline at zero in between

3. Full-Wave Rectification (Bridge Rectifier)

• Uses four diodes in bridge configuration:
  • Conducts during both half-cycles
  • Inverts negative half so all output pulses are positive

Graph:

• All sine peaks are upright
• No zero output periods (except at zero crossings)

4. Smoothing with a Capacitor

• Capacitor is added in parallel with the load resistor:
  • Charges during peak voltage
  • Discharges slowly during voltage dips → reduces fluctuations

Effectiveness depends on:

• Capacitance (C): Larger C = smoother output
• Load resistance (R): Larger R = slower discharge = smoother output

Graph:

• Smoothed waveform becomes more like DC with ripple
• Ripple size decreases with higher RC time constant

Note: Output is not pure DC but significantly smoothed