A large superconducting magnet, used for magnetic resonance...

Name: Problem 71, Chapter 23: College Physics for AP® Courses
Uploaded: 2019-10-19T20:51:40-08:00
Duration: 34 s
Channel: Charles Magnusen
Description: A large superconducting magnet, used for magnetic resonance imaging, has a 50.0 H inductance. If you want current through it to be adjustable with a 1.00 s characteristic time constant, what is the minimum resistance of system?

A large superconducting magnet, used for magnetic resonance imaging, has a 50.0 H inductance. If you want current through it to be adjustable with a 1.00 s characteristic time constant, what is the minimum resistance of system?

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Key Concepts

Inductance

Inductance is a component property that quantifies the ability of a circuit to store energy in its magnetic field when current flows through it. Measured in henries (H), inductance influences how quickly the current in a circuit can change, particularly during transient operations. It plays a critical role in determining the time constant when paired with resistance.

Resistance

Resistance opposes the flow of electric current and in the context of an RL circuit, it affects the rate at which current reaches its steady state following a transient event. By setting the desired time constant, the necessary minimum resistance can be calculated using the relation R = L/?, ensuring that the circuit responds at the intended rate.

RL Circuit Time Constant

The time constant (?) in an RL circuit is the time it takes for the current to reach approximately 63.2% of its final value after a sudden change, such as the application of a voltage step. This parameter is given by the formula ? = L/R, where L is the inductance and R is the resistance, and it is fundamental in analyzing the transient response of circuits.

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