Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 27, Problem 3OQ
To determine

The ranking of the given actions in terms of the change in current from greatest increase to the greatest decrease.

Expert Solution & Answer
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Answer to Problem 3OQ

The ranking of current in decreasing order is given by (c)>(a)>(b)>(e)>(d).

Explanation of Solution

Write the expression for the Ohm’s Law.

    V=IR                                                                                                               (I)

Here, R is the resistance, V is the voltage and I is the current.

Write the expression for the power in terms of voltage.

    P=V2R                                                                                                            (II)

Here, P is the power.

Write the expression for the resistance.

    R=ρlA                                                                                                         (III)

Here, R is the resistance, ρ is the resistivity, l is the length and A is the cross sectional area of the wire.

Write the expression for the current in terms of potential difference.

    I=VAVBR                                                                                                   (IV)

Here, VA is the potential at point A and VB is the potential at point B.

Write the expression for the resistance of the wire in terms of temperature.

    R=R0(1+αT)                                                                                               (V)

Here, R is the resistance at temperature T and α is the coefficient of temperature.

Case (a):

Substitute 50V for VA and 0V for VB in equation (IV) to find I1.

    I1=50V0VR=50VR

Substitute 150V for VA and 0V for VA in the equation (IV) to find I2.

    I2=150V0VR=150VR=3×50VR

Substitute 50VR for I1 in the above equation to find I1.

    I2=3I1

Therefore, the current is I2=3I1.

Case (b):

Rearrange equation (II) to find voltage.

    V=PR

Write the expression for the ratio of the voltages at power P1 and P2.

    V1V2=P1P2

Substitute 3P1 for P2 in the above equation.

    V1V2=P13P1V1V2=13V2=3V1

Substitute I2R for V2 and I1R for V1 in the above equation to find I2.

    I2=I13

Therefore, the value of current for triple power is I2=I13.

Case (c):

Substitute equation (III) in equation (I) to find V1.

    V1=ρI1lA1

Substitute πr12 for A1 in the above equation.

    V1=ρI1lπr12

Write the expression for voltage V2.

    V2=ρI2lπr22

Write the expression for the ratio of V1 and V2.

    V1V2=(ρI1lπr12)(ρI2lπr22)=r22I2r12I1

Substitute 2r1 for r2 in the above expression.

    V1V2=4I2I1

Therefore, the current is I2=4I1.

Case (d):

Substitute equation (III) in equation (I) to find V1.

    V1=ρI1lA1

Write the expression for voltage V2.

    V2=ρI2lA2

Write the expression for the ratio of voltage V1 and V2.

    V1V2=(ρI1lA1)(ρI2lA2)=I1l1I2l2

Substitute 2l1 for l2 in the above equation.

    V1V2=I1l1I22l1=I12I2

Therefore, then current is I2=12I1.

Case (e):

From equation (V), it is clear that resistance is proportional to temperature T.

Hence, when temperature is doubled, the resistance is also doubled.

The ratio of voltages from equation (I) is given by:

    V1V2=Ι1R1I2R2

Substitute 2R1 for R2 in the above equation, we get,

    V1V2=Ι1R1I22R1=I12I2

Therefore, the current is I2=12I1.

Conclusion:

Therefore, the ranking of current in the decreasing order is given by (c)>(a)>(b)>(e)>(d).

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Chapter 27 Solutions

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

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Ohm's law Explained; Author: ALL ABOUT ELECTRONICS;https://www.youtube.com/watch?v=PV8CMZZKrB4;License: Standard YouTube License, CC-BY