Tutorial 1 A - Alternating Current

Learning Objective

Recall the nature of alternating current and compare it to direct current.

Recognise and use technical terms associated with AC.

Key Questions

What is AC?

How do we measure AC?

Why do we use AC?

 

AC and DC

Direct current  from a battery moves in one direction only, from positive to negative.  In alternating current the direction is changing all the time. 

 

In Europe the frequency  is 50 Hz (cycles per second).  DC is good for Electronic devices.  But AC is much more easily distributed than DC.

 

The graph below shows the difference between AC and DC.

   

Note from this graph:

  • One complete alternation is called a cycle (NOT wavelength).

  •  The frequency is the number of cycles per second.  Units are hertz (Hz).

  •  The period is the time taken for one cycle.  It is measured in seconds. 

  • The current follows exactly the same wave form as the voltage.

 

Period equation:

f = 1/T.

 

The symbol for an ac supply is shown here.

 

Root Mean Square Value

We can measure AC voltages in three ways:

·       Measure the peak to peak voltage, easily done on a cathode ray oscilloscope (CRO).

·       Work out the  peak voltage which is half the peak-to-peak voltage.

·       Measure the root mean square (rms) value, or the effective value.  This is what we get if we use a voltmeter.

This is what we see on a CRO screen:

 

Equations:

 

V0 = Vpk to pk

          2

 

Vrms = V0

           √2

 

 

Question 1

What is the peak voltage of the mains, Vrms = 230 V?                               

Answer

 

We use the rms value because its use allows us to do electrical calculations as if they were direct currents.

 

Heating effect of AC   
The RMS voltage and currents are the “DC equivalents”.  We know that P = VI, so, if we plot a graph showing the voltage, current, and power, we see:

The average p.d  and the average current would be zero but this is not very useful – energy is obviously being transferred so, to get some idea of an ‘average’, it is useful to look at the power delivered.

 Deriving the equation:

 Power: 

P = IV = I0V0 = Pmax

 For the peak current:

I0 =  I rms × √2

  If I = 0, power = 0

  The mean power:

Pav = Pmax ÷ 2

The root mean square value of I for a.c. Irms, is the current (dc) that would give the same power as the mean (ac) power

 Irms 2  = Io2 ÷ 2

 Irms   = Io ÷ √2

 Also   Vrms = Vo ÷ √2                      

e.g. for the mains, V0  = 325 V  so Vrms =  230 V

 

Now go on to Tutorial 1 B about the Oscilloscope.  Press the Next button below.

Question 2

How does the power vary with time if a current of Irms passes through a heater with a voltage of Vrms?  Think about the power when V and I are positive and when V and I are negative. 

Answer

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