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?

466.67 s or 7.78 min

Explanation:

Applying,

E = LdI/dtEquation 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.