- 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]
- (Im/T) [-1+1]
- => Iavg = 0.
Note:- Value of alternating current keeps on changing.
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?
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
= 2.20 A
(b) The net power consumed over a full cycle is given as:
P = VI = 220 × 2.2 = 484 W