Chapter 30: Q89P (page 902)

A coil with an inductance of 2.0H and a resistance of $10 Ω$ is suddenly connected to an ideal battery with $ε = 100 V$ . (a) What is the equilibrium current? (b) How much energy is stored in the magnetic ﬁeld when this current exists in the coil?

Short Answer

Expert verified

The equilibrium current is $i_{0} = 10 A$
The amount of energy is stored in the magnetic field when the current exists in the coil $U_{B} = 100 J$

Step by step solution

Given

The inductance of a coil is L = 2.0 H
The resistance of a coil is $R = 10 Ω$
The emf of an ideal battery is $ε = 100 V$

Understanding the concept

We need to use the equation of Ohm’s law to calculate the equilibrium current and the equation of energy stored in the magnetic field of an inductor.

Formulae:

$i_{0} = \frac{E}{R} U_{B} = \frac{1}{2} L i_{0}^{2}$

(a) Calculate the equilibrium current

According to Ohm’s law, the equilibrium current through the coil is

$i_{0} = \frac{ε}{R} i_{0} = \frac{100 V}{10 Ω} i_{0} = 10 A$

(b) Calculate the amount of energy is stored in the magnetic field when the current exists in the coil

The expression for the magnetic energy is

$U_{B} = \frac{1}{2} L i_{0}^{2} U_{B} = \frac{1}{2} \times 2.0 H \times {(10 A)}^{2} U_{B} = 100 J$

Amount of energy stored in the magnetic field is 100J

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A coil with an inductance of 2.0H and a resistance of $10 Ω$ is suddenly connected to an ideal battery with $ε = 100 V$ . (a) What is the equilibrium current? (b) How much energy is stored in the magnetic ﬁeld when this current exists in the coil?

Short Answer

Step by step solution

Given

Understanding the concept

(a) Calculate the equilibrium current

(b) Calculate the amount of energy is stored in the magnetic field when the current exists in the coil

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A coil with an inductance of 2.0H and a resistance of10Ωis suddenly connected to an ideal battery withε=100V. (a) What is the equilibrium current? (b) How much energy is stored in the magnetic ﬁeld when this current exists in the coil?

Short Answer

Step by step solution

Given

Understanding the concept

(a) Calculate the equilibrium current

(b) Calculate the amount of energy is stored in the magnetic field when the current exists in the coil

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Energy Physics

Further Mechanics and Thermal Physics

Wave Optics

Work Energy and Power

Medical Physics

Nuclear Physics

Study anywhere. Anytime. Across all devices.

A coil with an inductance of 2.0H and a resistance of $10 Ω$ is suddenly connected to an ideal battery with $ε = 100 V$ . (a) What is the equilibrium current? (b) How much energy is stored in the magnetic ﬁeld when this current exists in the coil?