AC Circuit: RMS & Mean Current Explained

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SUMMARY

In AC circuits, RMS (Root Mean Square) current is defined as I/sqrt(2), which represents the effective value of alternating current for calculating power dissipation. The mean current, derived from the average of the instantaneous power equation P = i²R, provides insight into energy dissipation over time. The average value of the sin² function is 0.5, leading to the conclusion that the average power dissipated in a resistor is P_avg = I²R/2. This RMS value is essential for practical applications in electronics.

PREREQUISITES
  • Understanding of AC circuit fundamentals
  • Knowledge of sinusoidal waveforms
  • Familiarity with power calculations in electrical engineering
  • Basic mathematics involving trigonometric functions
NEXT STEPS
  • Study the derivation of RMS values in AC circuits
  • Explore power factor and its impact on AC circuit efficiency
  • Learn about the differences between RMS and average current in various waveforms
  • Investigate practical applications of RMS current in electronic devices
USEFUL FOR

Electrical engineers, electronics technicians, and students studying AC circuit theory will benefit from this discussion on RMS and mean current definitions and their applications.

saiaspire
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Hello people,

In an AC circuit, how is RMS current and Mean current defined as?
What is the practical meaning of RMS current?

Thanks in advance.
 
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Well, in an AC circuit the current is alternating back and forth. So:

P = i^{2}R = (Isin(\omega t - \phi))^{2}R = I^{2}Rsin^{2}(\omega t - \phi)

This is the instantaneous rate at which energy is dissipated in the resistor. So the average rate at which energy is dissipated in the resistor is the average of this equation over time.

The average value of a sin^2 graph is 0.5. So:

P_{avg} = I^{2}R/2 = (I/\sqrt{2})^{2}R

So the quantity I/sqrt2 is called the root mean square or RMS value of the current I.

So if we use RMS current we can find the average rate of energy dissipation in an AC circuit.

This is what's usually used in electronics related work.
 

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