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8 April, 15:03

The superconducting magnet in a magnetic resonance imaging system consists of a solenoid with 5.6 H of inductance. The solenoid is energized by connecting it to a 1.2 V DC power supply. Starting from zero, how long does it take for the solenoidto reach its operating current of 100 A?

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  1. 8 April, 15:57
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    466.67 s or 7.78 min

    Explanation:

    Applying,

    E = LdI/dt ... Equation 1

    Where E = Energized E. m. f in the solenoid, dI = change in current, dt = change in time.

    make dt the subject of the equation,

    dt = Ldi/E ... Equation 2

    Given: L = 5.6 H, dI = 100-0 = 100 A, E = 1.2 V

    Substitute into equation 2

    dt = 5.6 (100) / 1.2

    dt = 560/1.2

    dt = 466.67 s

    dt = (466.67/60) min = 7.78 min

    Hence, it takes 466.67 s or 7.78 min for the solenoid to reach its operating current.
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