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An inductor with an inductance of 2.50 $\mathrm{H}$ and a resistor with a resistance of 8.00$\Omega$ are connected to the terminals of a battery with an emf of 6.00 $\mathrm{V}$ and negligible internal resistance. Find (a) the initial rate of increase of the current in the circuit, (b) the initial potential difference across the inductor, (c) the current 0.313 s after the circuit is closed, and (d) the maximum current.

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a. 2.40 $\mathrm{A} / \mathrm{s}$b. 6.00 $\mathrm{V}$c. 0.474 $\mathrm{A}$d. 0.750 $\mathrm{A}$

Physics 102 Electricity and Magnetism

Chapter 21

Electromagnetic Induction

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Inductance

Alternating Current

Cornell University

Rutgers, The State University of New Jersey

McMaster University

Lectures

03:27

Electromagnetic induction is the production of an electromotive force (emf) across a conductor due to its dynamic interaction with a magnetic field. Michael Faraday is generally credited with the discovery of electromagnetic induction in 1831.

08:42

In physics, a magnetic field is a vector field that describes the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter (usually in the cgs system of units) and B is measured in teslas (SI units).

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An inductor with an induct…

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A $10.0-\mathrm{V}$ batter…

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A $10.0$ - $V$ battery, a …

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For the $R L$ circuit show…

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But this problem, we haven't r l circuit. The resistance is eight homes. The induct Ince's 2.5 Henry's and the IMF is six votes. Our first task is to find the initial rate of change of the current. So to do this, we want to call on our voltage Lou plot. So we want to trace a loop around this circuit and account for each of the voltage drops or gains. So we start with the IMF, we're gonna go up by the M f and then just going clockwise. We're going to go down by the resistance so that voltage drop is I r. And then down the inductive. It's so that voltage is l times. The change in current over the change in time and all of that gets us back to our initial point. So that gives a syrup now, Initially, when this first begins, there is no current the current zero, so we can disregard this second term zero. So this tells us that our E M f is equal to l don't The kind of the tea or our initial changing rate of that current is our EMF over are inducted. Now what is this that it's six votes divided by 2.5 Henry's. And that gets us 2.40 amps per second. The second part. We want to find the voltage drop across the induct in CE right after this begins. So we know that Ah, the voltage drop across the resistance is zero. Because that current is zero. So we actually have this answer in hurt, eh? Where we have our EMF being equal Thio though the idol t and that is our voltage drop across the inductions. So that is six boats for part C. We want to know what the current is at time. T equals 0.313 seconds after this, we want to call on our equation oven R l circuit. We know that the current is a function of time is given by our mm over our resistance. And this is multiplied by one minus e to the negative or time constant are over. L multiplied by t. Now we're told. Evaluate this at T equals 0.313 seconds. So we'll plug everything in. You have six forts divided by eight homes, one minus eat the negative. The um's over 2.5 Henry's and then this is multiplied by 0.313 seconds. And if we plug this in up to three significant figures, we have 0.475 amps. Lastly for part D, we want to know what our maximum current is. So in this time equation for the current we can think about our maximum time is when t goes to infinity so t goes to infinity. You know that you, to the minus are over l a times t goes to zero, which means that I goes to you're our which we will call our maximum current, and that is equal to six votes divided by eight homes. So we have a maximum current of 0.750 amps.

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