Question

The equation for alternating voltage is given by :

• A. e = Em Cos \(\omega\)t
• B. e = Em Sin \(\omega\)t
• C. e = Em tan \(\omega\)t
• D. e = Em cosec \(\omega\)t

Hint:

Sinusoidal functions (\(\sin \omega t\)) are used to model alternating current and voltage because they represent the smooth rotation of a generator armature.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
An alternating voltage (AC voltage) is an electrical voltage that reverses its direction periodically and varies in magnitude continuously over time, typically following a sinusoidal waveform.
Detailed Explanation:
The generation of alternating voltage in an AC generator is based on Faraday's Law of Electromagnetic Induction.
As a coil rotates at a constant angular velocity \(\omega\) inside a uniform magnetic field, the magnetic flux linking the coil varies sinusoidally.
The instantaneous induced electromotive force (EMF), \( e \), at any time \( t \) is given by the sinusoidal equation:
\[ e = E_m \sin(\omega t) \] Where:
- \( e \) is the instantaneous alternating voltage at time \( t \).
- \( E_m \) is the maximum amplitude or peak voltage.
- \(\omega\) is the angular frequency of rotation (\(\omega = 2\pi f\)).
- \( t \) is the elapsed time.
While a cosine wave can also represent an alternating wave (shifted by \(90^{\circ}\)), the standard convention starting from \( t = 0 \) is represented by the sine function, making Option (B) the correct choice.

Step 2: Final Answer:
The standard equation for alternating voltage is \( e = E_m \sin \omega t \).