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Found in: Page 862

### College Physics (Urone)

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

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# Camera flashes charge a capacitor to high voltage by switching the current through an inductor on and off rapidly. In what time must the $$0.100{\rm{ }}A$$ current through a $$2.00{\rm{ }}mH$$ inductor be switched on or off to induce a $$500{\rm{ }}V$$ emf?

In $$\Delta t = 4 \cdot {10^{ - 4}}{\rm{ }}ms$$ the $$0.100{\rm{ }}A$$ current through a $$2.00{\rm{ }}mH$$ inductor must be switched on or off to induce a $$500{\rm{ }}V$$ emf.

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## Step 1: Concept Introduction

A current produced by the creation of voltage (electromotive force) in the presence of a shifting magnetic field is known as electromagnetic induction.

This happens when a conductor is placed in a magnetic field that is moving (using an AC power source) or when a conductor is continuously moving in a magnetic field that is stationary

## Step 2: Information Provided

• Current in the inductor: $$0.100{\rm{ }}A$$.
• Self-inductance of the inductor: $$\begin{array}{c}2.00{\rm{ }}mH = \frac{{2.00}}{{1000}}\\ = 0.002{\rm{ }}H\end{array}$$.
• EMF of the inductor to be induced: $$500{\rm{ }}V$$.

## Step 3: Calculation for time –

The absolute value of the electromotive force produced when an inductor's current varies is given by –

$$\varepsilon = M\frac{{\Delta I}}{{\Delta t}}$$

It will take a certain amount of time for a certain current shift to occur in a certain inductance in order to generate a certain electromotive force –

$$\Delta t = \frac{{M\Delta I}}{\varepsilon }$$

After substituting the values –

\begin{align}{}\Delta t &= \frac{{0.002 \cdot 0.1}}{{500}}\\ &= 4 \cdot {10^{ - 7}}{\rm{ }}s\\ &= 4 \cdot {10^{ - 7}} \times 1000{\rm{ }}s\\ &= 4 \cdot {10^{ - 4}}{\rm{ }}ms\end{align}

Therefore, the value for time is obtained as $$\Delta t = 4 \cdot {10^{ - 4}}{\rm{ }}ms$$.

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