Root mean square (r.m.s.) voltages and currents
The r.m.s. value of an a.c. signal is equal to the value of direct current (d.c.) which would have the same effect or energy change as the a.c.
For example if a 12 voltUnit of voltage. For example, the voltage across the lamp was 6 volts (V). car battery operated a light bulb of powerThe energy transferred each second, measured in watts (W). Power = work done 梅 time taken. 36 wattThe unit of power. with direct current, an a.c. supply would need to be set to 12 V r.m.s. to achieve the same 36 W power output.
The r.m.s. voltage of an a.c. signal is always less than peak voltage because the peak voltage only occurs twice in the cycle (one positive one negative, during the rest of the cycle). At other times it is less!
To calculate the r.m.s. voltage from the peak voltage the factor of \(\frac{1}{\sqrt2}\) is used.
\(V_{rms}=\frac{V_{peak}}{\sqrt2}\)
There is a similar relationshipA relationship tells us how two or more variables work together, eg the relationship between resistance, voltage and current is: resistance = voltage 梅 current. between r.m.s. and peak current.
\(I_{rms}=\frac{I_{peak}}{\sqrt2}\)
For example the mains voltage in the UK can vary between 216 and 253 volts. These are r.m.s. values. To calculate the maximum possible voltage from a mainsThe name given to the electricity from a wall socket. Eg: The mains voltage is 230V. socket the peak voltage for 253 volts r.m.s. is:
\(V_{peak}=\sqrt2\,V_{rms}\)
\(=1.41\times253\)
\(V_{peak} = 358V\)
All mains appliances must be designed to operate safely at this peak voltage even though it only happens twice every 0.02 seconds!
Question
How does the peak power developed by an a.c. appliance compare to the r.m.s. power?
Peak power is twice the r.m.s. power.
\(Power=current\times voltage\). If both \(I\) and \(V\) are multiplied by \(\sqrt 2\) then the overall factor is \(2\).
Some audio devices are advertised with peak to peak power outputs which can appear to be four times the actual r.m.s. power output. Peak power is measured from zero line to the peak value but 'peak to peak' is measured from the trough to the peak ie double the peak power.