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Alternating Current & Voltage (CIE A Level Physics)

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Properties of alternating current & voltage

  • 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 time period of an alternating current is defined as:

T space equals space 1 over f

  • Where:
    • T = time period (s)
    • f = frequency (Hz)
  • 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

Time period and peak current on a current-time graph

Alternating current graph, downloadable AS & A Level Physics revision notes

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

Worked example

The variation with time t of the output voltage V of an alternating voltage supply is shown in the graph below.

Worked example voltage graph, downloadable AS & A Level Physics revision notes

Use the graph to calculate the frequency of the supply.

Answer:

Step 1: Write down the period-frequency relation

f space equals space 1 over T

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 is

T = 0.2 ms = 0.2 × 10-3 s

Step 3: Substitute into frequency equation

f space equals space fraction numerator space 1 over denominator 0.2 space cross times space 10 to the power of negative 3 end exponent end fraction space equals space 5000 space Hz space equals space 5 space kHz

Examiner Tip

Remember to double check the units on the alternating current and voltage graphs. These are often shown in the range of milli-seconds (ms) instead of seconds (s) on the x axis.

Using sinusoidal representations

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

I space equals space I subscript 0 sin open parentheses omega t close parentheses

  • 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 space equals space V subscript 0 sin open parentheses omega t close parentheses

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

omega space equals space fraction numerator 2 pi over denominator T end fraction space equals space 2 pi f

  • Where:
    • f = frequency of the supply (Hz)

Worked example

An alternating current I varies with time t as shown in the graph below.

21-1-1-we-alternating-current--cie-new

Using the graph and the equation for alternating current, calculate the value of the current at a time 0.48 s.

Answer:

Step 1: Write out the equation for alternating current

I space equals space I subscript 0 sin open parentheses omega t close parentheses

Step 2: Write out the equation for angular frequency

omega space equals fraction numerator space 2 pi over denominator T end fraction

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

I space equals space I subscript 0 sin open parentheses omega t close parentheses space equals space I subscript 0 sin open parentheses fraction numerator 2 pi t over denominator T end fraction close parentheses

I space equals space 17 sin open parentheses fraction numerator 2 pi open parentheses 0.48 close parentheses over denominator 0.1 end fraction close parentheses space equals space minus 16.168 space equals space minus 16 space straight A space open parentheses 2 space straight s. straight f close parentheses

Examiner Tip

These equations are written as  x space equals space x subscript 0 sin open parentheses omega t close parentheses, the x is replaced with I or V, depending on the question.

Remember to check that your calculator is in radians mode when using any of these equations. This is because the angular frequency is measured in rad s-1.

Current can also be positive or negative, depending on its direction. This is why the answer in the worked example is negative. At t = 0.48 s the current will be in the negative direction. The mark schemes in the exams are normally not too picky about this, but the size of the current (16 A in the worked example) is what will get the mark.

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Ashika

Author: Ashika

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Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.