Physics Alternating Current ETEA 2011
PMDC Verified Question 118 of 127
The sinusoidal alternating voltage can be expressed by the equation \(V = V_m \cos \omega t\). The instantaneous value of alternating voltage at \(t = 3T/4\) is:
A
\(V_m\)
B
\(-V_m\)
C
Zero
D
None of these
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: Zero
Concept:

The instantaneous value is found by substituting the time \(t\) and \(\omega = \frac{2\pi}{T}\) into the given cosine waveform equation.

Formula / Reaction:

$$V(t) = V_m \cos(\omega t) = V_m \cos\left(\frac{2\pi}{T} \cdot t\right)$$

Solution:

  • At \(t = \frac{3T}{4}\):


  • \(\theta = \omega t = \left(\frac{2\pi}{T}\right) \left(\frac{3T}{4}\right) = \frac{3\pi}{2} = 270^\circ\).


  • \(V = V_m \cos(270^\circ) = V_m (0) = 0\).


Why other options are incorrect:

  • Opt_A: \(+V_m\) occurs at \(t = 0\) and \(t = T\).


  • Opt_B: \(-V_m\) occurs at \(t = T/2\) (\(\theta = \pi\)).


  • Opt_D: Option C is the exact mathematical result.

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