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College Physics (Urone)
Found in: Page 863

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Short Answer

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

The minimum resistance of system is \(50\Omega \).

See the step by step solution

Step by Step Solution

Step 1: Concept Introduction

Resistance is a measurement of the resistance to current flow in an electrical circuit. Resistance in ohms is denoted by the Greek letter omega \(\left( \Omega \right)\). Ohms are named after Georg Simon Ohm \(\left( {1784 - 1854} \right)\), a German scientist who studied the relationship between voltage, current, and resistance.

Step 2: Information Provided

  • Inductance of the magnet: \(50.0{\rm{ }}H\)
  • The time constant value: \(1.00{\rm{ }}s\)

Step 3: Calculating Minimum Resistance

In \(RL\) systems, the time constant is given as

\(\tau = \frac{L}{R}\)

This means that given a time constant and inductance, the value of the resistor in the

system may be calculated as follows:

\(R = \frac{L}{\tau }\)

Numerically, in our case, we will have

\(\begin{array}{c}R = \frac{{50}}{1}\\ = 50\Omega \end{array}\)

Therefore, the required solution is \(50\Omega \).

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