Answer to Question #117591 in Electric Circuits for Ben

Question

Using your AC graph, add an appropriate scale on the vertical axis and label the ‘peak voltage value’ and ‘RMS voltage value’. Explain why RMS voltage value is more useful than the peak value. Show, by calculation, the peak voltage value if the effective voltage value in the UK is 230V.

Answer 1

Attempts to find an average value of AC would directly provide you the answer zero... Hence, RMS values are used. They help to find the effective value of AC (voltage or current).

This RMS is a mathematical quantity (used in many math fields) used to compare both alternating and direct currents (or voltage). In other words (as an example), the RMS value of AC (current) is the direct current which when passed through a resistor for a given period of time would produce the same heat as that produced by alternating current when passed through the same resistor for the same time.

Practically, we use the RMS value for all kinds of AC appliances. The same is applicable to alternating voltage also. We're taking the RMS because AC is a variable quantity (consecutive positives and negatives). Hence, we require a mean value of their squares thereby taking the square root of sum of their squares

from the above graph we can see that

$V_{rms}=0.707V_{peak}$

$230=0.707V_{peak}\\V_{peak}=325.3Volts$