Question

Alternating voltage \((V)\) is represented by the equation

• A. \(V(t)=V_m e^t\)
• B. \(V(t)=V_m\sin \omega t\)
• C. \(V(t)=V_m\cot \omega t\)
• D. \(V(t)=V_m\tan \omega t\)

Hint:

Standard alternating voltage is represented by: \[ V=V_m\sin\omega t \] or \[ V=V_m\cos\omega t \]

Answer 1

The Correct Option is B

Concept:
Alternating voltage is a voltage whose magnitude and direction change periodically with time. The most common form of alternating voltage is sinusoidal. The standard equation is: \[ V(t)=V_m\sin\omega t \] where, \[ V(t)=\text{instantaneous voltage} \] \[ V_m=\text{maximum or peak voltage} \] \[ \omega=\text{angular frequency} \] \[ t=\text{time} \]

Step 1: Understand alternating voltage.
In direct voltage, the polarity remains fixed. But in alternating voltage, the polarity changes repeatedly after equal intervals of time. This periodic variation is usually represented by a sine or cosine function.

Step 2: Recall standard AC equation.
The standard sinusoidal voltage is: \[ V=V_m\sin\omega t \] It may also be written as: \[ V=V_m\cos\omega t \] depending on the reference phase.

Step 3: Check the given options.
Option (A) \(V(t)=V_me^t\) represents exponential growth, not alternating voltage.
Option (B) \(V(t)=V_m\sin\omega t\) is the standard form of alternating voltage.
Option (C) \(V(t)=V_m\cot\omega t\) is not used for AC voltage.
Option (D) \(V(t)=V_m\tan\omega t\) is also not the standard AC expression. Hence, the correct answer is: \[ \boxed{(B)\ V(t)=V_m\sin\omega t} \]