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Chapter 20: Problem 51

The current in a \(0.080-\mathrm{H}\) solenoid increases from \(20.0 \mathrm{mA}\) to \(160.0 \mathrm{mA}\) in \(7.0 \mathrm{s} .\) Find the average emf in the solenoid during that time interval.

Short Answer

Expert verified
Answer: The average electromotive force (emf) in the solenoid during the given time interval is -1.6 V.

Step by step solution

01

Convert values to proper units

To work with the given values, let's convert all currents to amperes (A) and make sure all other units are in SI units. Initial current: \(I_1 = 20.0 \mathrm{mA} = 20.0 \times 10^{-3} A\) Final current: \(I_2 = 160.0 \mathrm{mA} = 160.0 \times 10^{-3} A\) Inductance: \(L = 0.080 H\) Time interval: \(\Delta t = 7.0 s\)
02

Calculate change in current

Calculate the change in current by subtracting the initial current from the final current: \(\Delta I = I_2 - I_1 = (160.0 - 20.0) \times 10^{-3} A = 140 \times 10^{-3} A\)
03

Plug values into Faraday's law formula

Plug the given values into Faraday's law formula to find the average emf: \(\text{average emf} = \frac{-L \Delta I}{\Delta t} = \frac{-(0.080 H)(140 \times 10^{-3} A)}{7.0 s}\)
04

Calculate the average emf

Now calculate the average emf: \(\text{average emf} = \frac{-(0.080 H)(140 \times 10^{-3} A)}{7.0 s} = -1.6 V\) The average electromotive force (emf) in the solenoid during the given time interval is \(-1.6 V\). The negative sign indicates that the emf is acting against the change in current.

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Most popular questions from this chapter

A de motor is connected to a constant emf of \(12.0 \mathrm{V}\) The resistance of its windings is \(2.0 \Omega .\) At normal operating speed, the motor delivers \(6.0 \mathrm{W}\) of mechanical power. (a) What is the initial current drawn by the motor when it is first started up? (b) What current does it draw at normal operating speed? (c) What is the back emf induced in the windings at normal speed?
A \(0.30-\mathrm{H}\) inductor and a \(200.0-\Omega\) resistor are connected in series to a \(9.0-\mathrm{V}\) battery. (a) What is the maximum current that flows in the circuit? (b) How long after connecting the battery does the current reach half its maximum value? (c) When the current is half its maximum value, find the energy stored in the inductor, the rate at which energy is being stored in the inductor, and the rate at which energy is dissipated in the resistor. (d) Redo parts (a) and (b) if, instead of being negligibly small, the internal resistances of the inductor and battery are \(75 \Omega\) and \(20.0 \Omega\) respectively.
A transformer for an answering machine takes an ac voltage of amplitude $170 \mathrm{V}\( as its input and supplies a \)7.8-\mathrm{V}$ amplitude to the answering machine. The primary has 300 turns. (a) How many turns does the secondary have? (b) When idle, the answering machine uses a maximum power of \(5.0 \mathrm{W}\). What is the amplitude of the current drawn from the 170 -V line?
A solenoid of length \(2.8 \mathrm{cm}\) and diameter \(0.75 \mathrm{cm}\) is wound with 160 turns per cm. When the current through the solenoid is $0.20 \mathrm{A},$ what is the magnetic flux through one of the windings of the solenoid?
A coil of wire is connected to an ideal \(6.00-\mathrm{V}\) battery at \(t=0 .\) At \(t=10.0 \mathrm{ms},\) the current in the coil is \(204 \mathrm{mA}\) One minute later, the current is 273 mA. Find the resistance and inductance of the coil. [Hint: Sketch \(I(t) .]\)
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