Alternating Current

voltage

time0

maximum positive voltage (the peak voltage)

maximum negative voltage (peak voltage)

Direction of current and size constantly change. Mains frequency is 50 Hz

Alternating Current 2

Voltage(V)

Time (s)

0

peak voltage

effective voltage

The quoted value ( rms ) or Effective voltage of an a.c. supply is the same as the steady d.c. voltage which would produce the same heating effect in a resistance wire.

The quoted value of the mains voltage in the UK is 230 V. The peak voltage is 325 V.

Effective voltage is measured with a voltmeter. Peak voltage is measured with an oscilloscope.

Alternating Current 3The quoted value of an a.c. supply is also known as the r.m.s. value (root mean square). The peak value is √2 larger than this r.m.s. value. This applies to both voltage and current.

peaksmrpeaksmr IIandVV2

1

2

1......

Voltage

Time

peak value

r.m.s value

Alternating Current 4

2peak

rms

II

AI rms 83.2

Peak and r.m.s. values: Example The period of a sinusoidally varying current is 0.005 s. The peak value of the current is 4·0 A.

Calculate a) the frequencyb) the root mean square value of the current.

Frequency = 1 / Period

Frequency = 1 / 0.005

Frequency = 200 Hz 2

4rmsI

Calculation of frequency

timebase

(s cm –1 )

y input0.02

Find the time for one wave.

This is the period.

frequency = 1/period

ExampleTime base = 0.02 s cm-1

Period = time base setting x no of boxes for 1 cycle

Period = 0.002 x 4 = 0.08 s

Frequency = 1 / period

Frequency = 1 / 0.08 = 12.5 Hz.