EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
6th Edition
ISBN: 9781319321710
Author: Mosca
Publisher: VST
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Chapter 28, Problem 63P

(a)

To determine

The initial rate of increase of current.

(a)

Expert Solution
Check Mark

Answer to Problem 63P

The initial rate of increase of current is 3kA/s .

Explanation of Solution

Given:

The inductance of a coil is L=4mH

The resistance of a resistor is R=150Ω

The voltage of ideal battery is εo=12V

Formula used:

The expression for the current in the circuitis given by,

  I=εo(1e t τ )R

Calculation:

The initial rate of increase of current is calculated by differentiating the current with time.

  dIdt=εoRddt(1e t τ )=εoR(e t τ )( 1τ)=εoRτe tτ

Solve further as,

  dIdt t=0=εoRτe 0τ=12V4mH=3kA/s

Conclusion:

Therefore, the initial rate of increase of current is 3kA/s .

(b)

To determine

The rate of increase of current when the current is half of its steady-state value

(b)

Expert Solution
Check Mark

Answer to Problem 63P

The rate of increase of current when the current is half of its steady-state value is 1.5kA/s .

Explanation of Solution

Formula used:

The expression for the current in the circuit is given by,

  I=εo(1e t τ )R

Calculation:

According to the given condition,

  I=0.5IfIIf=1e tτ0.51=e tτe tτ=0.5

The rate of increase of current at I=0.5If is calculated by differentiating the current with time.

  dIdt=εoRddt(1e t τ )=εoR(e t τ )( 1τ)=εoRτe tτ

Solve further as,

  dIdt=0.5×εoL=0.5×12V4mH=1.5kA/s

Conclusion:

Therefore, the rate of increase of current when the current is half of its steady-state value is 1.5kA/s .

(c)

To determine

The steady state value of current.

(c)

Expert Solution
Check Mark

Answer to Problem 63P

The steady state value of current is 0.08A .

Explanation of Solution

Formula used:

The expression for the steady state value of current is given by,

  If=εoR

Calculation:

The steady state value of current is calculated as,

  If=εoR=12V150Ω=0.08A

Conclusion:

Therefore, the steady state value of current is 0.08A .

(d)

To determine

The time taken of the current to reach 99% of its steady-state value

(d)

Expert Solution
Check Mark

Answer to Problem 63P

The time taken of the current to reach 99% of its steady-state value is 0.123ms .

Explanation of Solution

Formula used:

The expression for the current in the circuit is given by,

  I=εo(1e t τ )R

Calculation:

According to the given condition,

  I=0.99IfIIf=1e tτ0.991=e tτe tτ=0.01

Solve further as,

  t=τln(0.01)=LRln(0.01)=4mH150Ωln(0.01)=0.123ms

Conclusion:

Therefore, the time taken of the current to reach 99% of its steady-state value is 0.123ms .

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Chapter 28 Solutions

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