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Ch 30: Inductance
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 30: InductanceProblem 7a
Chapter 30, Problem 7a

At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude of the self-induced emf is 0.0160 V. What is the inductance of the inductor?

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1
Understand the relationship between the self-induced emf (ε), the inductance (L), and the rate of change of current (di/dt) in an inductor, which is given by the formula: ε = -L didt.
Identify the given values from the problem: the self-induced emf (ε) is 0.0160 V, and the rate of change of current (di/dt) is 0.0640 A/s.
Rearrange the formula to solve for the inductance (L): L = -εdidt.
Substitute the given values into the rearranged formula: L = -0.01600.0640.
Calculate the value of L using the substituted values to find the inductance of the inductor.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inductance

Inductance is a property of an electrical conductor that quantifies its ability to induce an electromotive force (emf) when the current flowing through it changes. It is measured in henries (H) and is determined by the physical characteristics of the conductor, such as its shape and the material it is made from.
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Self-Induced EMF

Self-induced emf is the voltage generated within an inductor due to a change in current flowing through it. According to Faraday's law of electromagnetic induction, this emf is proportional to the rate of change of current and the inductance of the coil, described by the formula emf = -L * (di/dt), where L is inductance and di/dt is the rate of change of current.
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Rate of Change of Current

The rate of change of current refers to how quickly the current flowing through a circuit changes over time, typically measured in amperes per second (A/s). This rate is crucial in determining the self-induced emf in an inductor, as a faster change in current results in a greater emf, according to the relationship emf = -L * (di/dt).
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Related Practice
Textbook Question

The inductor shown in Fig. E30.11 has inductance 0.260 H and carries a current in the direction shown. The current is changing at a constant rate. The potential between points a and b is Vab = 1.04 V, with point a at higher potential. Is the current increasing or decreasing?

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Textbook Question

At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude of the self-induced emf is 0.0160 V. If the inductor is a solenoid with 400 turns, what is the average magnetic flux through each turn when the current is 0.720 A?

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Textbook Question

Two coils have mutual inductance M = 3.25 × 10-4 H. The current i1 in the first coil increases at a uniform rate of 830 A/s. What is the magnitude of the induced emf in the second coil? Is it constant?

Textbook Question

When the current in a toroidal solenoid is changing at a rate of 0.0260 A/s, the magnitude of the induced emf is 12.6 mV. When the current equals 1.40 A, the average flux through each turn of the solenoid is 0.00285 Wb. How many turns does the solenoid have?

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Textbook Question

A 2.50-mH toroidal solenoid has an average radius of 6.00 cm and a cross-sectional area of 2.00 cm2. How many coils does it have? (Make the same assumption as in Example 30.3.)

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