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Chapter 23: Q66PE (page 863)

How fast can the \(150{\rm{ }}A\) current through a \(0.250{\rm{ }}H\) inductor be shut off if the induced emf cannot exceed \(75.0{\rm{ }}V\)?

Short Answer

Expert verified

The time in which current through a inductor can be shut off is \(500\;ms\).

Step by step solution

01

Concept Introduction

A passive electrical component that dampens current variations is an inductor. Other names for inductors are coils and chokes. In electrical nomenclature, the letter \(L\) stands in for an inductor

02

Information Given

  • The current value:\(150{\rm{ }}A\)
  • The inductance value:\(0.250{\rm{ }}H\)
  • The emf value: \(75.0{\rm{ }}V\)
03

Calculating the Force

Whenthecurrentinaninductorchange,weknowthattheinducedelectromotiveforceisgivenby

\(\varepsilon = \frac{{L\Delta I}}{{\Delta t}}\)

Asaresult,whentheotherfactorsareknown,wecansolveforthetime.

\(L = \frac{{\varepsilon \Delta t}}{{\Delta I}}\)

Numerically, we will have

\(\begin{array}{c}\Delta t = \frac{{0.25 \times 150}}{{75}}\\ = 0.5\;s\end{array}\)

Therefore, the required solution is \(500\;ms\).

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Most popular questions from this chapter

(a) An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner’s 2.00 T field with his fingers pointing in the direction of the field. Find the average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) Discuss whether this current would significantly change the temperature of the ring.

Verify, as was concluded without proof in Example\(23.7\), that units of

\(\begin{align}{}T \times {m^2}{\rm{ }}/{\rm{ }}A{\rm{ }} & {\rm{ }}\Omega \times s{\rm{ }}\\ & = {\rm{ }}H\end{align}\).

When the \(20.0{\rm{ }}A\) current through an inductor is turned off in \(1.50{\rm{ }}ms\), an \(800{\rm{ }}V\) emf is induced, opposing the change. What is the value of the self-inductance?

(a) Calculate the self-inductance of a \({\rm{50}}{\rm{.0}}\)cm long, \({\rm{10}}{\rm{.0}}\)cm diameter solenoid having \({\rm{1000}}\) loops. (b) How much energy is stored in this inductor when \({\rm{20}}{\rm{.0}}\) A of current flows through it? (c) How fast can it be turned off if the induced emf cannot exceed \({\rm{3}}{\rm{.00}}\)V?

(a) Use the exact exponential treatment to find how much time is required to bring the current through an\({\rm{80}}{\rm{.0 mH}}\)inductor in series with a\({\rm{15}}{\rm{.0 \Omega }}\)resistor to\({\rm{99}}{\rm{.0\% }}\)of its final value, starting from zero. (b) Compare your answer to the approximate treatment using integral numbers of\({\rm{\tau }}\). (c) Discuss how significant the difference is.
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