What is Root Mean Square Value of AC Signal?

Electrical4u
03/09/2024

These are the questions which come in our minds every time when we are dealing with AC circuits.

image.png

Suppose, we have a simple DC circuit (figure – 1) and we want to replicate it in an AC circuit. We got every thing same, except supply voltage which is now to be an AC supply voltage. Now, the question is what should be the value of AC supply voltage so that our circuit works exactly same as that of DC.

image.png

Let us put same value of AC supply voltage (AC Vpeak = 10 volt) which is in our DC circuit. By doing that we can see (figure 3) for a half cycle how the AC voltage signal is not covering up the whole area (blue area) of constant DC voltage, which means our AC signal can not supply the same amount of power as our DC supply.

Which means we must increase the AC voltage to cover the same area and see if it is supplying the same amount of power or not.
ac signal

We found that (figure 4) by increasing the peak voltage Vpeak up to (π/2) times of DC supply voltage we can actually cover the whole area of DC in AC. When the AC voltage signal completely represents the DC voltage signal then that value of DC signal is called the average value of AC signal.
ac signal
Now our AC voltage should supply the same amount of power. But when we switched-on the supply surprisingly, we found that AC voltage is supplying more power than the DC. Because an average value of AC supplies same amount of charges but not the same amount of power. So, to get same amount of power from our AC supply we must decrease our AC supply voltage.
ac signal
We found that by decreasing the peak voltage Vpeak up to √2 times DC voltage we get same amount of power flowing in both the circuits. When the AC voltage signal supply same amount of power as in DC then that value of DC voltage is called root mean square or rms value of AC.
We are always concerned about how much power is flowing through our circuits irrespective of how much electrons are needed to supply that power and that is the reason why we always use the rms value of AC supply instead of average value everywhere in AC system.

Conclusion
Average value of an AC current represent the equal amount of charges in DC current.

RMS value of an AC current represent the equal amount of power in DC current

AC current takes less amount of charges to supply the same amount of DC power.


Source: Electrical4u

Statement: Respect the original, good articles worth sharing, if there is infringement please contact delete.

Electrical4u

Electrical4U is dedicated to the teaching and sharing of all things related to electrical and electronics engineering.

What is a Pure Resistive AC Circuit?
What is a Pure Resistive AC Circuit?
Pure Resistive AC CircuitA circuit containing only a pure resistanceR(in ohms) in an AC system is defined as a Pure Resistive AC Circuit, devoid of inductance and capacitance. Alternating current and voltage in such a circuit oscillate bidirectionally, generating a sine wave (sinusoidal waveform). In this configuration, power is dissipated by the resistor, with voltage and current in perfect phase—both reaching their peak values simultaneously. As a passive component, the resistor neither
Edwiin
06/02/2025
What is a Pure Capacitor Circuit?
What is a Pure Capacitor Circuit?
Pure Capacitor CircuitA circuit comprising only a pure capacitor with capacitanceC(measured in farads) is termed a Pure Capacitor Circuit. Capacitors store electrical energy within an electric field, a characteristic known ascapacitance(alternatively referred to as a "condenser"). Structurally, a capacitor consists of two conductive plates separated by a dielectric medium—common dielectric materials include glass, paper, mica, and oxide layers. In an ideal AC capacitor circuit, the current
Edwiin
06/02/2025
Resistance Switching in a Circuit Breaker
Resistance Switching in a Circuit Breaker
Resistance SwitchingResistance switching refers to the practice of connecting a fixed resistor in parallel with the contact gap or arc of a circuit breaker. This technique is applied in circuit breakers with high post-arc resistance in the contact space, primarily to mitigate re-striking voltages and transient voltage surges.Severe voltage fluctuations in power systems arise from two main scenarios: interrupting low-magnitude inductive currents and breaking capacitive currents. Such overvoltages
Edwiin
05/23/2025
What is Biot Savart Law?
What is Biot Savart Law?
The Biot-Savart Law is employed to determine the magnetic field intensity dHnear a current-carrying conductor. In other words, it describes the relationship between the magnetic field intensity generated by a source current element. This law was formulated in 1820 by Jean-Baptiste Biot and Félix Savart. For a straight wire, the direction of the magnetic field adheres to the right-hand rule. The Biot-Savart Law is also referred to as Laplace’s law or Ampère’s law.Conside
Edwiin
05/20/2025
Inquiry
Download
IEE-Business is dedicated to serving the personnel in the global power industry.
Join IEE-Business, not only can you discover power equipment and power knowledge, but also canhnd like - minded friends!