Direct current sources provide a constant voltage and current over time, making it easy to measure
In situations involving alternating voltage and current, the average values of voltage and current will?always be zero
This can make it difficult to measure
The mean value for alternating current and voltage is always zero
The use of?root mean square?values gets around this problem
First remove all the negative signs by simply squaring the peak current, or voltage
Find the average of the squared value
And finally, take the square root
Root-mean-square (rms) values of current, or voltage, are a useful way of?comparing?a.c current, or voltage, to its equivalent direct current (d.c), or voltage
The rms values represent the direct current, or voltage, values that will produce the same?heating effect, or power dissipation, as the alternating current, or voltage
The rms value of an alternating current is defined as:
The square root of the mean of squares of all the values of the current in one cycle
An alternate definition is:
The equivalent direct current that produces the same power
A resistive load is any electrical component with resistance eg. a lamp
Vrms?and peak voltage. The rms voltage is about 70% of the peak voltage
Worked Example
An electric oven is connected to a 230 V root mean square (rms) mains supply using a cable of negligible resistance.
Calculate the peak-to-peak voltage of the mains supply.
Step 1: Write down the Vrms equation
Exam Tip
Remember to double-check the units on the alternating current and voltage graphs. These are often shown in milliseconds (ms) instead of seconds (s) on the x-axis.
Average Power Calculations
The average?power?of a supply is the product of the rms current and voltage:
Average power?= Irms?× Vrms
Worked Example
What is the maximum current supplied to a 2300 W kettle which is connected to an a.c. supply of peak voltage 325 V?