Class 12 Physics Alternating Current | RMS voltage |

**RMS voltage**

- RMS means Root Mean Squared voltage. This means taking the root of the mean of the square of the instantaneous voltage.
- RMS voltage is also known as
__Effective voltage__which is defined as the overall effective value of the alternating current or alternating voltage. - Square root of the mean of the squared function of instantaneous values.
- For example V
_{1}^{2}, V_{2}^{2}, V_{3}^{2}, V_{4}^{2}are the instantaneous values of voltages. - Therefore V
_{rms }= √( V_{1}^{2}+ V_{2}^{2 }+ V_{3}^{2}+ V_{4}^{2})/4 - It supplies the same power to the load as an equivalent DC circuit. P = I
_{rms}^{2}R. - This means the power which is supplied to the load will be equivalent to the DC circuit.

__Graphically:-__

- The RMS value of an alternating voltage will correspond to the same amount of power consumption in case of DC voltage.
- Therefore RMS is known as effective value of the alternating voltage. This shows DC voltage and RMS voltage will supply the same power in both the cases.

This RMS value will correspond to the same amount of power consumption that will be same in case of DC

** Problem:**-

(a) The peak voltage of an AC supply is 300 V. What is the rms voltage?

(b) The rms value of current in an AC circuit is 10 A. What is the peak current?

** Answer** :-

(a) Peak voltage of the ac supply, V_{o} = 300 V

rms voltage is given as:

V = (V_{o}/√2)

= (300 /√2)

= 212.1 V

(b) The rms value of current is given as:

I = 10 A

Now, peak current is given as:

I_{o} = √2I = √2 × 10 = 14.1 A

__Determining RMS voltages V _{rms}__

__Case 1__:- Instantaneous discrete values:- Values are each distinguishable from the other.

- Consider the discrete values of voltages at each specific instant of time t as V
_{1},V_{2},V_{3},--,V_{n}. - Therefore V
_{rms}= √( (V_{1}^{2 }+ V_{2}^{2 }+ V_{3}^{2}+ V_{4}^{2}+…+ V_{n}^{2})/n)

__Case2:__- Instantaneous continuous values :- Each instant of time is not distinguishable from other instant of time.

- V = V
_{m}sinωt this means voltage is changing at every moment. Voltage value is like a sine function. - V
_{rms}=√ ( (1/T)_{0}^{T}∫ (V^{2}dt)) - = √(1/T)
_{0}^{T}∫ V_{m}^{2}sin^{2}ωt dt - After simplifying the above equation:-
**V**_{rms}= (V_{m}/√2)

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