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 I
_{1}^{2}, I_{2}^{2}, I_{3}^{2},…., I_{n}^{2}are the instantaneous values of currents. - I
_{rms }= √(=√( I_{1}^{2}+I_{2}^{2}+ I_{3}^{2}+I…. + I_{n}^{2})/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 = I
_{m}sinωt . - Therefore
**I**_{rms}= (Im/√2) .

**Overview of I _{rms}, I_{avg}, I_{inst}**

Instantaneous value of current :-

- I = I
_{m}sinωt. As (ωt) keeps changing therefore the value of I keeps on changing. - At every instant the value of current is changing.
- I
_{m}= maximum or peak value that current can take.

RMS value :-

- I
_{rms}= (I_{m}/ √2) . - The RMS value is the effective value of alternating current .

Average value of current:-

- I
_{avg}means the average value of current over one complete cycle. - I
_{avg}= 0. - => I
_{avg }= (1/T)_{0}^{T}∫ I dt - = (1/T)
_{0}^{T}∫ I_{m}sinωt dt (Using I = I_{m}sinωt) - => (I
_{m}/T) [-cosωt + cos0]

After Simplifying,

- (I
_{m}/T) [-1+1] - => I
_{avg }= 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

.