Virtual or effective value of a.c.

The virtual or effective value of an a.c. is defined as the steady current which would produce the same heating effect in a given resistance as the a.c. itself.

Mathematically, the virtual value of a.c. is given by,

Vrms = √(1/T ∫T0 V(t)² dt)

Where V(t) is the instantaneous voltage at time t, T is the time period of the a.c. and the integration is taken over one complete cycle.

Options given

a) -0.637I0
b) -0.707I0
c) 0.637I0
d) 0.707I0

Correct answer

The correct answer is option 'D' i.e. 0.707I0.

Explanation

- The virtual or effective value of an a.c. is always positive and it is given by the root mean square (rms) value of the a.c.
- The rms value of an a.c. is always the ratio of the peak value of the a.c. and the square root of 2.
- Mathematically, the rms value of an a.c. is given by,

Vrms = Vp/√2

Where Vp is the peak value of the a.c.

- For a sine wave, the peak value is √2 times the virtual value, which means,

Vp = √2 Vrms

- Substituting this value of Vp in the above equation, we get,

Vrms = Vp/√2 = (√2 Vrms)/√2 = Vrms

- Therefore, the virtual value or effective value of a sine wave is equal to its rms value.
- In the given options, option 'D' i.e. 0.707I0 represents the rms value of the a.c. which is equal to its virtual value.
- Hence, the correct answer is option 'D' i.e. 0.707I0.