Class 12 Physics Alternating Current RMS Current

RMS Current

  • RMS current is same as Root Mean Squared current. It is the effective current.
  • Square root of the mean of the squared function of instantaneous values.
    • For example I12, I22, I32,….,  In2   are the instantaneous values of currents.
    • Irms = √(=√( I12+I22+ I32+I…. + In2)/n   (For discrete values of current)
  • It supplies the same power to the load  as an equivalent DC circuit.
  • In case of continuous values :-   I = Im sinωt .
  • Therefore Irms= (Im/√2) .

 

Overview of  Irms, Iavg, Iinst

Instantaneous value of current :-

  • I = Im sinωt. As (ωt) keeps changing therefore the value of I keeps on changing.
  • At every instant the value of current is changing.
  • Im = maximum or peak  value that current can take.

RMS value :-

  • Irms = (Im/ √2) .
  • The RMS value is the effective value of alternating current .

Average value of current:-

  • Iavg means the average value of current over one complete cycle.
  • Iavg = 0.
  • => Iavg = (1/T) 0T ∫ I dt
  • = (1/T) 0T ∫ Im  sinωt  dt  (Using  I = Im sinωt)
  • => (Im/T) [-cosωt + cos0]

After Simplifying,

  • (Im/T) [-1+1]
  • => Iavg = 0.

Note:- Value of alternating current keeps on changing.

 

Problem:-

A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.

(a) What is the rms value of current in the circuit?

(b) What is the net power consumed over a full cycle?

 

Answer:-

Resistance of the resistor, R = 100 Ω

Supply voltage, V = 220 V

Frequency, ν = 50 Hz

(a) The rms value of current in the circuit is given as

I=(V/R)

= (220)/(100)

 = 2.20 A

(b) The net power consumed over a full cycle is given as:

P = VI = 220 × 2.2 = 484 W 

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