An alternating voltage is given by E=100sin⁡ω+π6V . The voltage will be maximum for the first time when is (T = periodic time)

MHT CET · Physics · Alternating Current

An alternating voltage is given by $E = 100 \sin (ω + \frac{π}{6}) V$ . The voltage will be maximum for the first time when is (T = periodic time)

A $\frac{T}{12}$
B $\frac{T}{2}$
C $\frac{T}{6}$
D $\frac{T}{3}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{T}{6}$

Step-by-step Solution

Detailed explanation

Given, alternating voltage is

E = 100 \sin (ω t + \frac{π}{6}) V

The voltage will be maximum, when

\sin (ω t + \frac{π}{6}) = 1

\Rightarrow \sin (ω t + \frac{π}{6}) = s i n \frac{π}{2}

\Rightarrow ω t + \frac{π}{6} = \frac{π}{2}

\Rightarrow ω t = \frac{π}{3}

\Rightarrow t = \frac{π}{3 ω} = \frac{π \times T}{3 \times 2 π} [∵ ω = \frac{2 π}{T}]

= \frac{T}{6}

Thus, the voltage will be maximum for the first time when t =

\frac{T}{6}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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