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Maximum emf in a coil from the mutual inductance and a sinusoidal current

This type of question, asked 10 times: 9 May 2023 S1, 10 May 2023 S1, 15 May 2023 S1, 9 May 2024 S2, 12 May 2024 S1, 11 Apr 2026 S2, 13 Apr 2026 S1, 16 Apr 2026 S2, 18 Apr 2026 S1, 14 May 2026 S1. All 10 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    21
    Two coils have a mutual inductance 5×10−3 H5 \times 10^{-3}\,\text{H}. The current changes in the first coil according to the equation I1=I0sin⁡ωtI_1 = I_0\sin\omega t where I0=10 AI_0 = 10\,\text{A} and ω=100π rad/s\omega = 100\pi\,\text{rad/s}. What is the value of the maximum e.m.f. in the coil?

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  2. Question 2

    10 May 2023 S1

    23
    Two coils have a mutual inductance 0.003 H. The current changes in the first coil according to equation I=I0sin⁡ωtI=I_0\sin\omega t, where I0=8 AI_0=8\,\text{A} and ω=100π rad s−1\omega=100\pi\,\text{rad\,s}^{-1}. The maximum value of e.m.f. in the second coil is

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  3. Question 3

    15 May 2023 S1

    44
    Alternating current of peak value 2π\frac{2}{\pi} A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is 1 H. The peak e.m.f. induced in secondary coil (Frequency of a.c. =50= 50 Hz)

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  4. Question 4

    9 May 2024 S2

    1
    Two coils A and B have mutual inductance 0.0080.008 H. The current changes in the coil A, according to the equation I=Imsin⁡ωtI = I_m \sin\omega t, where Im=5I_m = 5 A and ω=200π\omega = 200\pi rad s−1^{-1}. The maximum value of the e.m.f. induced in the coil B in volt is

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  5. Question 5

    12 May 2024 S1

    50
    Two coils have a mutual inductance of 0.004 H. The current changes in the first coil according to equation I=I0sin⁡ωtI=I_{0}\sin\omega t, where I0=10 AI_{0}=10\,\text{A} and ω=50π rad s−1\omega=50\pi\,\text{rad\,s}^{-1}. The maximum value of e.m.f. in the second coil in volt is

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  6. Question 6

    11 Apr 2026 S2

    139
    Alternating current of peak value (2π)\left(\dfrac{2}{\pi}\right) A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is 11 H. The peak em.f. induced in secondary coil is (Frequency of a. c. is 5050 Hz)

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  7. Question 7

    13 Apr 2026 S1

    135
    Two coils P and Q have mutual inductance 'M' H. If the current in the coil P is I=I0sin⁡ωtI = I_0\sin\omega t, then the maximum value of e.m.f. induced in coil Q is

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  8. Question 8

    16 Apr 2026 S2

    137
    Alternating current of peak value (2π)\left(\dfrac{2}{\pi}\right) A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is 1H. The peak value of induced e.m.f. in the secondary coil is (Frequency of a.c. = 50 Hz)

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  9. Question 9

    18 Apr 2026 S1

    136
    Two coils have a mutual inductance of 0.0050.005 H. The current changes in the first coil according to equation I=I0sin⁡ωtI = I_0\sin\omega t, where I0=10I_0 = 10 A and ω=60π rad s−1\omega = 60\pi\ \mathrm{rad\,s^{-1}}. The maximum values of e.m.f. in the second coil in volt will be

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  10. Question 10

    14 May 2026 S1

    135
    A current i=10sin⁡(100πt)i = 10\sin(100\pi t) A is passed in first coil, which induces a maximum e.m.f. 5π5\pi V in second coil. The mutual inductance between the coils is

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