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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# 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 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 $$50\Omega$$.