Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Question: Unreasonable Results
(a) On a particular day, it takes \(9.60 \times {10^3}\;J\) of electric energy to start a truck's engine. Calculate the capacitance of a capacitor that could store that amount of energy at \(12.0\;V\).
(b) What is unreasonable about this result?
(c) Which assumptions are responsible?

The capacitance of a capacitor that could store that amount of energy at \(12.0\;V\) is \(133\;\;F\).
A capacitor of capacitance \(133\;\;F\) might be too big in phrases of dimensions to be carried at the truck.
It is unreasonable to expect that the capacitor can keep that quantity of electrical energy.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Concepts and Principles

The following is the amount of energy held in a capacitor with capacitance \(C\) that is charged to a potential difference \(\Delta V\): \({U_E} = \frac{1}{2}C{(\Delta V)^2}...(1)\).

Step 2: Given Data

The electric energy required to start the engine is: \({U_E} = 9.60 \times {10^3}\;J\).
The potential difference across the capacitor is: \(\Delta V = 12.0\;V\).

Step 3: Finding Energy stored

The energy stored in the capacitor is found from Equation \((1)\):

\({U_E} = \frac{1}{2}C{(\Delta V)^2}\)

Solve for \(C\):

\(C = \frac{{2{U_E}}}{{{{(\Delta V)}^2}}}\)

Entering the values for \({U_E}\) and \(\Delta V\), we obtain:

\(\begin{aligned}{}C = \frac{{2\left( {9.60 \times {{10}^3}\;J} \right)}}{{12.0\;V}}\\ = 133\;\;F\end{aligned}\)

Therefore, the capacitance value is obtained as \(133\;\;F\).

Step 4: Explanation for part (b)

A capacitor of capacitance \(133\;\;F\)might be too big in phrases of dimensions to be carried at the truck.

Step 5: Explanation for part (c)

It is unreasonable to expect that the capacitor can keep that quantity of electrical energy

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Short Answer

Step by Step Solution

Step 1: Concepts and Principles

Step 2: Given Data

Step 3: Finding Energy stored

Step 4: Explanation for part (b)

Step 5: Explanation for part (c)

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College Physics (Urone)

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Short Answer

Step by Step Solution

Step 1: Concepts and Principles

Step 2: Given Data

Step 3: Finding Energy stored

Step 4: Explanation for part (b)

Step 5: Explanation for part (c)

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