II Magnetic resonance imaging instruments use very large...

II Magnetic resonance imaging instruments use very large magnets that consist of many turns of superconducting wire. A typical such magnet has an inductance of $40 \mathrm{H.}$ When the magnet is initially powered up, the current through it must be increased slowly so as not to "quench" the wires out of their superconducting state. One such magnet is specified to have its current increased from 0 A to 150 A over 200 min. What con- stant voltage needs to be applied to yield this rate?

II Magnetic resonance imaging instruments use very large magnets that consist of many turns of superconducting wire. A typical such magnet has an inductance of $40 \mathrm{H.}$ When the magnet is initially powered up, the current through it must be increased slowly so as not to "quench" the wires out of their superconducting state. One such magnet is specified to have its current increased from 0 A to 150 A over 200 min. What con-
stant voltage needs to be applied to yield this rate?

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Key Concepts

Electromagnetic Inductance

Inductance is the property of an electrical component (typically a coil) that causes it to oppose changes in current by creating an induced voltage. It is quantified by the constant L, and the relationship is captured by the equation V = L(dI/dt), where V is the voltage and dI/dt is the rate of change of current.

Rate of Change of Current

The rate of change of current, denoted as dI/dt, is a critical concept in time-dependent circuit analysis. It describes how rapidly current changes over time, and in inductive circuits, this rate of change is directly proportional to the voltage applied across the inductor.

Constant Voltage in Inductive Systems

When a constant voltage is applied to an inductor, the relationship V = L(dI/dt) implies that the current increases at a constant rate. This principle is essential for designing circuits where a gradual increase in current is required, such as in systems using superconducting magnets where sudden surges must be avoided.

Time Unit Conversion in Circuit Analysis

Correct unit conversion, such as converting minutes into seconds, is fundamental in circuit calculations to ensure consistency with SI units. This enables accurate application of mathematical relationships in the analysis and design of electrical systems.

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