# Comparing rms value and peak value of AC

##### Demonstration

This experiment helps advanced level students to compare qualitatively the power produced by AC and equivalent DC sources. Root mean square (rms) values of AC voltage are calculated from peak values measured by an oscilloscope.

#### Apparatus and materials

Power supply, low-voltage, AC

Cells, 1.5 V, 2

Lamp, 2.5 V in holder

Rheostat (10 - 15 ohms)

Two-way switch

#### Health & Safety and Technical notes

Oscilloscopes contain high voltages and often have ventilation holes which allow access to points which are 'hazardous live'. Warn classes not to poke anything through holes in the case.

A video available at the National STEM Centre e.library shows how to use an oscilloscope.

#### Procedure

a Connect a 2 V AC supply to a small lamp. Attach a crocodile clip to one lead, to act as a home-made two-way switch.

b Connect the two dry cells and a rheostat to the lamp. The two-way switch gives a choice between the two supplies. Adjust the rheostat so that, with the DC supply, the lamp glows with the same brightness as with the AC supply.

c Connect leads also from the lamp to the y-input of the CRO with the time-base on.

d Switch to and fro between the two supplies, to make the comparison. With DC you will see the trace deflected upward (or down); with AC you will see the waveform. Are the AC waveform peaks higher than the steady DC voltage?

e Switch off the time-base of the oscilloscope, and centre the spot. In the DC case the spot will be deflected a definite amount. In the AC case, a line is obtained, the length of which is 2√2 times the deflection of the spot in the DC.

#### Teaching notes

If, you measure from the zero axis, then the AC peak value should be √2 the DC value for the same brightness of the lamp.

Frequency is the number of complete cycles of current or voltage per second measured in hertz. The frequency of the AC mains is 50Hz.

Peak voltage is measured from the zero axis to the top of the curve and in the case of the UK mains supply is 324 volts (√2 x 230 V).

Average voltage is zero.

Root mean square (average) voltage - the alternating current does not warm up a lamp as well as a direct current of the same value as the peak AC, so you need to work out how to find the equivalent DC voltage for the AC situation. The experiment shows the same heating effect from an AC peak voltage √2 times bigger than the equivalent DC voltage. The constant voltage giving the same power dissipation as the time-averaged power dissipation of a sinusoidal AC voltage is called VRMS.
Vpeak = √2VRMS

This experiment was safety-tested in January 2007