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Time for an alternating voltage or current to reach a given value in its cycle

This type of question, asked 10 times: 2 May 2023 S1, 16 May 2023 S1, 19 Apr 2025 S1, 22 Apr 2025 S2, 13 Apr 2026 S1, 16 Apr 2026 S1, 14 May 2026 S1, 14 May 2026 S2, 15 May 2026 S2, 19 May 2026 S1. All 10 questions below, oldest first.

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  1. Question 1

    2 May 2023 S1

    8
    In an a.c. circuit I=100sin⁡(200πt)I = 100\sin(200\pi t). The time required for the current to achieve its peak value will be

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  2. Question 2

    16 May 2023 S1

    46
    The alternating voltage is given by v=v0sin⁡(ωt+π/3)v = v_0\sin(\omega t + \pi/3), when will the voltage be maximum for first time?

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  3. Question 3

    19 Apr 2025 S1

    47
    The instantaneous value of current in an a.c. circuit is I=3sin⁡(50πt+π4)I= 3\sin\left( 50\pi t+\frac{\pi}{4} \right) A. The current will be maximum for the first time at

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  4. Question 4

    22 Apr 2025 S2

    40
    An alternating e.m.f. is given by e=e0sin⁡ωte =e_{0}\sin\omega t. In how much time the e.m.f. will have half its maximum value, if e starts from zero ? ( T=T = Time Period, sin⁡30∘=12\sin30^{\circ}=\frac{1}{2} )

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  5. Question 5

    13 Apr 2026 S1

    138
    An alternating e.m.f. is given by e=e0sin⁡ωte = e_0\sin\omega t. In what time the e.m.f. will have half its maximum value, if 'e' starts from zero? (sin⁡30∘=0.5)(\sin 30^\circ = 0.5)

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  6. Question 6

    16 Apr 2026 S1

    138
    An alternating e.m.f. is given by e=e0sin⁡ωte = e_0\sin\omega t. In what time the e.m.f. will have half its maximum value, if 'e' Starts from zero?

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  7. Question 7

    14 May 2026 S1

    139
    A resistance of 20 Ω20\,\Omega is connected to a source of alternating potential V=220sin⁡(100πt)V = 220\sin(100\pi t). The time taken by current to change from its peak value to r.m.s. value is (sin⁡π4=12)\left(\sin\dfrac{\pi}{4} = \dfrac{1}{\sqrt{2}}\right)

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  8. Question 8

    14 May 2026 S2

    137
    An alternating voltage is E=100sin⁡(ωt+π6)E = 100\sin\left(\omega t + \dfrac{\pi}{6}\right) V. The voltage will be maximum for the first time when t is (sin⁡π2=1)\left(\sin\dfrac{\pi}{2} = 1\right) (T = Periodic time)

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  9. Question 9

    15 May 2026 S2

    137
    An AC source is 120120 V - 6060 Hz. The value of voltage after 1720\dfrac{1}{720} s from start will be (sin⁡30∘=12)\left(\sin 30^\circ = \dfrac{1}{2}\right)

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  10. Question 10

    19 May 2026 S1

    138
    An alternating voltage is given by V=V0sin⁡(ωt+π4)V = V_0\sin\left(\omega t + \dfrac{\pi}{4}\right). The time when the voltage is maximum for the first time is (TT = periodic time of the alternating voltage, cos⁡0∘=sin⁡90∘=1\cos 0^\circ = \sin 90^\circ = 1)

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