Physics- Topic 21 (Alternating Currents)

Period of a current time graph

Is the time taken for one complete oscillation in the graph

T = 1/f

Peak Value

Is the maximum value in a graph

It can be determined from the amplitude of the graph

Sinusoidal Alternating Current or Voltage

General form= X=X₀sin(ωt )

where X0 is the peak value and ω is the angular frequency.

Root mean square values

X_rms = X₀/ √2, representing the effective value of an alternating current or voltage.

Mean Power in a Resistive Load

P=IV = I²R = V²R

I₀=√2 I_rms

P_peak=I₀²R = (√2 I_rms)²R = 2P_mean

P_mean = P_peak / 2

Rectification

Is the process of converting alternating current and the voltage into direct current and voltage

Full- wave Rectification Graph

The graph of the voltage V_out against time is a sine curve where the positive cycle and the negative cycle are both curved bumps

Half- wave Rectification graph

The graph of output voltage V_out against time is a sine curve where the positive cycles are curved bumps and the negative cycles are straight lines

Half wave rectification

• Consists of a single diode

  • AC supply is in series with diode and a resistor

• The diode will only conduct during the positive cycles of the ac supply

  • Current is only present when there is a positive cycle

• No negative cycles

• Half of the time, the voltage is Zero

  • Power available from a half-wave rectified circuit is reduced

Full- Wave Rectification

• Requires a bridge rectifier circuit

• During Positive cycles:

  • If one terminal is positive and the other supplies negative

  • Two diodes opposite each other will conduct

  • The other two diodes do not conduct

  • This causes the current to flow through the positive direction of the resistor

• Vice versa for the negative cycle

• Current is constant, and more power is supplied compared to half wave rectified circuit

Smoothing

The reduction in variation of the output in voltage or current

This is done using a smoothing capacitor

The single capacitor is connected in parallel with a load resistor

The capacitor charges up from the input voltage and maintains the voltage at a high level

As it discharges gradually through the resistor when rectified voltage drops but the voltage then rises again and the capacitor charges up again

Graphs before and after smoothing

Gives a ripple shape

Effects of single capacitor in smoothing

• The slower the capacitor discharges, the more the smoothing

• This can be using:

  • A capacitor with greater capacitance

  • A resistor with a high resistance

Recall t = RC

hence the time constant of the capacitor must be greater than the time interval between adjacent peaks of the output voltage