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An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is ______ μH.
(Round off to 2 decimal places.)
    Correct answer is between '50,52'. Can you explain this answer?
    Most Upvoted Answer
    An air-core radio-frequency transformer as shown has a primary winding...
    Concept:
    Mutual Inductance:

    When two coils are placed close to each other, a change in current in the first coil produces a change in magnetic flux, which cuts not only the coil itself but also the second coil as well. The change in the flux induces a voltage in the second coil, this voltage is called induced voltage and the two coils are said to have a mutual inductance.
    Consider a pair of coupled inductors with self-inductance L1 and L2, magnetically coupled through coupling coefficient k.

    Input and output voltage expressions are given as
    V1 = jωL1I1 + jωMI2   ...(1)
    V2 = jωL2I2 + jωMI1   ...(2)
    Where,
    ω = 2πf

    M = Mutual inductance
    L1 = Inductance of coil one
    L2 = Inductance of coil two
    Calculation:

    In the given circuit secondary is open-circuited, so I2 = 0 A
    Given secondary voltage V2 = 7.3 Vp-p
    The output voltage expression from equation(2) is given as
    V2 = jωMI1  ....(3)
    The given voltage across the 22 Ω resistor is 5 Vp-p
    So primary current is calculated as I1 = 5 / 22 Ap-p
    From equation(3)
    |V2| = 2π f M I1
    7.3 = 2 × π ×  100 × 103 × M × (5/22)
    M = 51.12 μH
    Free Test
    Community Answer
    An air-core radio-frequency transformer as shown has a primary winding...
    Concept:
    Mutual Inductance:

    When two coils are placed close to each other, a change in current in the first coil produces a change in magnetic flux, which cuts not only the coil itself but also the second coil as well. The change in the flux induces a voltage in the second coil, this voltage is called induced voltage and the two coils are said to have a mutual inductance.
    Consider a pair of coupled inductors with self-inductance L1 and L2, magnetically coupled through coupling coefficient k.

    Input and output voltage expressions are given as
    V1 = jωL1I1 + jωMI2   ...(1)
    V2 = jωL2I2 + jωMI1   ...(2)
    Where,
    ω = 2πf

    M = Mutual inductance
    L1 = Inductance of coil one
    L2 = Inductance of coil two
    Calculation:

    In the given circuit secondary is open-circuited, so I2 = 0 A
    Given secondary voltage V2 = 7.3 Vp-p
    The output voltage expression from equation(2) is given as
    V2 = jωMI1  ....(3)
    The given voltage across the 22 Ω resistor is 5 Vp-p
    So primary current is calculated as I1 = 5 / 22 Ap-p
    From equation(3)
    |V2| = 2π f M I1
    7.3 = 2 × π ×  100 × 103 × M × (5/22)
    M = 51.12 μH
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    An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is ______ μH.(Round off to 2 decimal places.)Correct answer is between '50,52'. Can you explain this answer?
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