• 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

Graph of alternating current against time with a time period of 20 ms and peak current of 2 A

• 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

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 equal 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 = V_0?sin(?t)

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

Step 1:??????????? Write out the equation for alternating current

I = I_0?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