Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Three wires, of the same diameter, are connected in turn between two points maintained at a constant potential difference. Their resistivity and lengths are p and L (wire A), 1.2p and 1.2 L (wire B), and 0.9p and L (wire C). Rank the wire according to the rate at which energy is transferred to thermal energy within them, greatest first.

The rank of the wires according to the rate at which the energy is transferred to the thermal energy within them, the greatest first is $P_{C} > P_{A} > P_{B}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

Three wires are of the same diameter and connected to the same potential difference.
Resistivity and length L of wire A is p and L
Resistivity and length L of wire B is 1.2p and 1.2L
Resistivity and length L of wire C is 0.9p and L

Step 2: Understanding the concept of rate of energy transfer

The rate of energy transfer or power is equal to the product of current and voltage.

We find the rank of the resistance of the wires using the formula of resistance. Then, using the relation between the resistance and the rate at which energy is transferred we can rank the wires according to the rate at which energy is transferred to the thermal energy within them, the greatest first.

Formulae:

The resistance value of a material, R = pL/A …(i)

Here, is resistance, is resistivity, L is the length of the conductor, A is the area of the cross-section of the conductor.

The rate of energy transferred per second, $P = V^{2} / R$ …(ii)

is energy transfer rate or power, V is potential difference, R is resistance.

Step 3: Calculation of the rank according to the energy transfer rate

From equation (i), we can get that the resistance value as follows:

$R α p L$ …(iii)

(Since,the same diameter of wires leads to same area.)

For wire A, the resistance can be given using equation (iii) for same area value as follows:

$R_{A} = \frac{p L}{A}$

For wire B, the resistance can be given using equation (iii) for same area value as follows:

$R_{B} = \frac{(1.2 p) (1.2 L)}{A} = 1.44 \frac{p L}{A}$

For wire C, the resistance can be given using equation (a) for same area value as follows:

$R_{C} = \frac{90.9) p L}{A} = 0.9 \frac{p L}{A}$

So, the resistance relation is $R_{B} > R_{A} > R_{C}$

But, from equation (ii), the rate of energy transfer per second can be given as:

$E α \frac{1}{R}$

So, the energy transfer rate relation is $P_{C} > P_{A} > P_{B}$

Therefore, the rank of the wires according to the rate at which energy is transferred to the thermal energy within them, the greatest first is $P_{C} > P_{A} > P_{B}$

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of rate of energy transfer

Step 3: Calculation of the rank according to the energy transfer rate

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of rate of energy transfer

Step 3: Calculation of the rank according to the energy transfer rate

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics