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Chapter 30: Q89P (page 902)

A coil with an inductance of 2.0H and a resistance of10惟is suddenly connected to an ideal battery with蔚=100V. (a) What is the equilibrium current? (b) How much energy is stored in the magnetic 铿乪ld when this current exists in the coil?

Short Answer

Expert verified
  1. The equilibrium current is i0=10A
  2. The amount of energy is stored in the magnetic field when the current exists in the coil UB=100J

Step by step solution

01

Given

  1. The inductance of a coil is L = 2.0 H
  2. The resistance of a coil is R=10惟
  3. The emf of an ideal battery is 蔚=100V
02

Understanding the concept

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

Formulae:

i0=ERUB=12Li02

03

(a) Calculate the equilibrium current

According to Ohm鈥檚 law, the equilibrium current through the coil is

i0=蔚Ri0=100V10惟i0=10A

04

(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

UB=12Li02UB=12脳2.0H脳(10A)2 UB=100J

Amount of energy stored in the magnetic field is 100J

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Most popular questions from this chapter

In Figure, 蔚=100V,R1=10.0惟,R2=20.0惟,R3=30.0惟,andL=2.00H.Immediately after switch S is closed, (a) what is i1? (b) what is i2? (Let currents in the indicated directions have positive values and currents in the opposite directions have negative values.) A long time later, (c) what is i1? (d) what is i2? The switch is then reopened. Just then, (e) what is i1? (f) what is i2? A long time later, (g) what is i1? (h) what is i2?

Att=0, a battery is connected to a series arrangement of a resistor and an inductor. If the inductive time constant is 37.0 ms, at what time is the rate at which energy is dissipated in the resistor equal to the rate at which energy is stored in the inductor鈥檚 magnetic field?

Question: At a certain place, Earth鈥檚 magnetic field has magnitudeB=0.590gaussand is inclined downward at an angle of 70.0掳to the horizontal. A flat horizontal circular coil of wire with a radius of 10.0 cmhas 1000 turnsand a total resistance of85.0惟. It is connected in series to a meter with140惟resistance. The coil is flipped through a half-revolution about a diameter, so that it is again horizontal. How much charge flows through the meter during the flip?

Att=0, a battery is connected to a series arrangement of a resistor and an inductor. At what multiple of the inductive time constant will the energy stored in the inductor鈥檚 magnetic field be 0.500its steady-state value?

Question: Figure (a) shows a wire that forms a rectangle ( W=20cm,H=30cm) and has a resistance of 5.0m惟. Its interior is split into three equal areas, with magnetic fields B1鈬赌,B2鈬赌andB3鈬赌 . The fields are uniform within each region and directly out of or into the page as indicated. Figure (b) gives the change in the z components localid="1661850270268" Bz of the three fields with time t; the vertical axis scale is set by localid="1661850263101" Bs=4.0渭罢andBb=-2.5Bs, and the horizontal axis scale is set by localid="1661850259349" ts=2.0s.

(a) What is magnitude of the current induced in the wire?(b) What is the direction of the current induced in the wire?
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