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Chapter 30: Q51P (page 899)

The current in an RL circuit drops from1.0 A to 10 mA in the first second following removal of the battery from the circuit. If L is10 H, find the resistance R in the circuit.

Short Answer

Expert verified

$R = 46 Ω$

Step by step solution

01

Given data

$i_{0} = 1 A$
$i = 10 \times 10^{- 3} A$

02

Understanding the concept

When the source of constant emf is removed, the current decays from a valueaccording to,

$i = i_{0} e^{\frac{- t}{τ_{L}}}$

Formulae:

The current decay in the RL circuit is given by,

$i = i_{0} e^{\frac{- t}{τ_{L}}}$

The inductive time constant is,

$τ_{L} = \frac{L}{R}$

03

Calculate the resistance R in the circuit

The current decay inRLcircuit is given by,

$\begin{array}{rcl} i & = & i_{0} e^{\frac{- t}{τ_{L}}} \\ \ln (\frac{i}{i_{0}}) & = & \frac{- t}{τ_{L}} \\ τ_{L} & = & \frac{- t}{\ln (\frac{i}{i_{0}})} \end{array}$

Hence,

$\frac{L}{R} = \frac{- t}{\ln (\frac{i}{i_{0}})}$

$\frac{10}{R} = \frac{- 1}{ln (\frac{10 \times 10^{- 3}}{1.0})}$

By solving for R,

$R = 46 Ω$

Therefore the resistance in the circuit is 46 ohm.

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Most popular questions from this chapter

The inductance of a closely packed coil of 400 turnsis 8.0 mH. Calculate the magnetic flux through the coil when the current is 5.0 mA.

Figure 30-29 shows three circuits with identical batteries, inductors, and resistors. Rank the circuits, greatest first, according to the current through the resistor labeled R (a) long after the switch is closed, (b) just after the switch is reopened a long time later, and (c) long after it is reopened

A toroidal inductor with an inductance of 9.0.mH encloses a volume of $0.0200 m^{3}$ . If the average energy density in the toroid is $70.0 J / m^{3}$ , what is the current through the inductor?

In Figure, a long rectangular conducting loop, of width L, resistance R, and mass m, is hung in a horizontal, uniform magnetic field $\vec{B}$ that is directed into the page and that exists only above line a. The loop is then dropped; during its fall, it accelerates until it reaches a certain terminal speed $v_{t}$ . Ignoring air drag, find an expression for $v_{t}$ .

A toroid has a 5.00 cmsquare cross section, an inside radius of 0.15m, 500turns of wire, and a current of 0.800A. What is the magnetic flux through the cross section?

See all solutions

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