Currents and Voltages In the voltage–time graph, the crest of the sine wave indicates the maximum voltage
reached.The maximum voltage is called the peak voltage (V0). For mains electricity, the alternating voltage varies periodically between 325 V and 325 V.
Mains electricity in Ireland is described as being 230 V. This means it has an equivalent heating effect of a 230 V d.c. supply. It should be clear from the graph that the average voltage is 0 V, as the graph is symmetrical with the same amount above as below the x-axis. Another way of saying that mains electricity in Ireland is equivalent to 230 V d.c. is to say that the average of the magnitude of the voltage is 230 V. In order to find the magnitude of the voltage at each instance, the voltage is squared to make it positive and then square rooted.The average (or mean) of these values can then be found. This value is called the root mean squared voltage (Vrms).
Because the voltage-time graph is sinusoidal2 the rms voltage can be calculated using the formula:
ALTERNATING VOLTAGE
Vrms root mean squared voltage, V0 peak voltage Vrms V0
12
As the current–time graph is also sinusoidal, the relationship between peak current (I0) and rms current (Irms) is:
ALTERNATING CURRENT
Irms root mean squared current, I0 peak current Irms I0
12
Fig 20.31: Current–time graph for a.c. is a sine wave
Current 0 Time
Voltage 0 Time
Fig 20.30:Voltage–time graph for a.c. is a sine wave
SAMPLE PROBLEM 20F The rms voltage of the mains electricity is 230 V. Calculate the peak voltage of the mains.
SAMPLE ANSWER 20F The peak voltage of the mains is 325 V.
Vrms V0 2The reason for the 12
12Q230 V0
12QV0 23012 325 V
Leaving Cert. course, but is on the website www.gillmacmillan.ie for illustrative purposes. 1
relates to the fact that the graph forms a sine wave; the justification is beyond the scope of the
