• An alternating current (a.c) is defined as:

A current which periodically varies from positive to negative and changes its magnitude continuously with time

• This means the direction of an alternating current varies every half cycle
• The variation of current, or p.d., with time can be described as a sine curve ie. sinusoidal
  • Therefore, the electrons in a wire carrying a.c. move back and forth with simple harmonic motion
• As with SHM, the relationship between time period T and frequency  f of an alternating current is given by:

• Peak current (I₀), or peak voltage (V₀), is defined as:

The maximum value of the alternating current or voltage

• Peak current, or voltage, can be determined from the amplitude of the graph

• Mains electricity is supplied as alternating current
  • Power stations produce alternating current
  • This is the type of current supplied when devices are plugged into sockets

Worked example: Calculating frequency

Step 1:           

Write down the period-frequency relation

Step 2:           

Calculate the time period from the graph

• • • The time period is the time taken for one complete cycle
    • From the graph this is equation to 0.2 ms
    • Therefore, the time period, T = 0.2 ms = 0.2 × 10^-3 s

Step 3:           

Substitute into frequency equation

• The equation representing alternating current which gives the value of the current I at any time t is:

I = I₀ sin(⍵t)

• Where:
  • I = current (A)
  • I₀ = peak current (A)
  • ⍵ = angular frequency of the supply (rad s^-1)
  • t = time (s)
• Note: this a sine function since the alternative current graph is sinusoidal
• A similar equation can be used for representing alternating voltage:

V = V₀ sin(⍵t)

• Where:
  • V = voltage (V)
  • V₀ = peak voltage (V)
• Recall the relation the equation for angular frequency ⍵:

Worked example: Using sinusoidal representations

Step 1:            Write out the equation for alternating current

I = I₀ sin(⍵t)

Step 2:            Write out the equation for angular frequency

Step 3:            Measure the time period T and peak current I₀ from the graph

The time period is the time taken for one full cycle, T = 0.10 s

Peak current (amplitude), I₀ = 17 A

Step 4:            Substitute values into alternating current equation at time t

Using the time given in the question, t = 0.48 s