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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

The windings of an electromagnet have inductance \(L=8.0 \mathrm{H}\) and resistance \(R=2.0 \Omega . \quad A \quad 100.0-V \quad d c\) power supply is connected to the windings by closing switch \(S_{2} .\) (a) What is the current in the windings? (b) The electromagnet is to be shut off. Before disconnecting the power supply by opening switch \(S_{2},\) a shunt resistor with resistance \(20.0 \Omega\) is connected in parallel across the windings. Why is the shunt resistor needed? Why must it be connected before the power supply is disconnected? (c) What is the maximum power dissipated in the shunt resistor? The shunt resistor must be chosen so that it can handle at least this much power without damage. (d) When the power supply is disconnected by opening switch \(S_{2},\) how long does it take for the current in the windings to drop to \(0.10 \mathrm{A} ?\) (e) Would a larger shunt resistor dissipate the energy stored in the electromagnet faster? Explain.
An ideal inductor of inductance \(L\) is connected to an ac power supply, which provides an emf \(\mathscr{E}(t)=\mathscr{E}_{\mathrm{m}}\) sin \(\omega t\) (a) Write an expression for the current in the inductor as a function of time. [Hint: See Eq. \((20-7) .]\) (b) What is the ratio of the maximum emf to the maximum current? This ratio is called the reactance. (c) Do the maximum emf and maximum current occur at the same time? If not, how much time separates them?
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