Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

(a) How much power is dissipated in a short circuit of \(240 - V\)\({\rm{AC}}\) through a resistance of \(0.250{\rm{ }}\Omega \)?
(b) What current flows?

\(P = 230\;kW\) is dissipated in a short circuit of \(240 - V\)\({\rm{AC}}\) through a resistance of \(0.250{\rm{ }}\Omega \).
The amount of current that flows is \(I = 960{\rm{ }}A\).

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Concept Introduction

If a potential difference \(\Delta V\) is maintained across a circuit element, the power or rate at which energy is supplied to the element, as,

\(P = I\Delta V\)

Because the potential difference across a resistor is given by \(\Delta V = IR\), we can express the power delivered to a resistor as,

\(\begin{align}{}P = {I^2}R\\ = \frac{{{{\left( {\Delta V} \right)}^2}}}{R}...(1)\end{align}\)

The energy delivered to a resistor be electrical transmission appears in the form of internal energy in the resistor.

Ohm's Law:

The current \(I\) through a circuit element (other than a battery) can be determined by dividing the potential difference \(\Delta V\) across the circuit element by its resistance \(R\) as,

\(I = \frac{{\Delta V}}{R}...\left( 2 \right)\)

Step 2: Information Provided

The potential difference across the circuit is: \(\Delta V = 240{\rm{ }}V\).
The resistance of the circuit is: \(R = 0.250{\rm{ }}\Omega \).

Step 3: Calculation for Power

The power dissipated in the circuit is found from Equation \((1)\)as,

\(P = \frac{{{{(\Delta V)}^2}}}{R}\)

Entering the values for \(\Delta V\) and \(R\), it is obtained as,

\(\begin{align}{}P &= \frac{{{{(240\;V)}^2}}}{{0.250{\rm{ }}\Omega }}\\& = 2.30 \times {10^5}\;W\\ &= \left( {2.30 \times {{10}^5}\;W} \right)\left( {\frac{{1\;kW}}{{1000\;W}}} \right)\\ &= 230\;kW\end{align}\)

Therefore, the value for the power is obtained as \(P = 230\;kW\).

Step 4: Calculation for Current

The current in the insulator is found by using Ohm's law from Equation \((2)\)as,

\(I = \frac{{\Delta V}}{R}\)

Entering the values for \(\Delta V\) and \(R\), it is obtained as,

\(\begin{align}{}I = \frac{{240{\rm{ }}V}}{{0.250{\rm{ }}\Omega }}\\ = 960{\rm{ }}A\end{align}\)

Therefore, the value of the current is obtained as \(I = 960{\rm{ }}A\).

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College Physics (Urone)

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Short Answer

(a) How much power is dissipated in a short circuit of \(240 - V\)\({\rm{AC}}\) through a resistance of \(0.250{\rm{ }}\Omega \)?
(b) What current flows?

Step by Step Solution

Step 1: Concept Introduction

Step 2: Information Provided

Step 3: Calculation for Power

Step 4: Calculation for Current

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College Physics (Urone)

Answers without the blur.

Short Answer

(a) How much power is dissipated in a short circuit of \(240 - V\)\({\rm{AC}}\) through a resistance of \(0.250{\rm{ }}\Omega \)? (b) What current flows?

Step by Step Solution

Step 1: Concept Introduction

Step 2: Information Provided

Step 3: Calculation for Power

Step 4: Calculation for Current

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(a) How much power is dissipated in a short circuit of \(240 - V\)\({\rm{AC}}\) through a resistance of \(0.250{\rm{ }}\Omega \)?
(b) What current flows?