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A 5.00$\mu \mathrm{F}$ capacitor is initially charged to a potential of 16.0 $\mathrm{V}$ . It is then connected in series with a 3.75 $\mathrm{mH}$ inductor. (a) What is the total energy stored in this circuit? (b) What is the maximum current in the inductor? What is the charge on the capacitor plates at the instant the current in the inductor is maximal?

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a. the energy stored in the circuit is $[0.64 \mathrm{mJ}]$b. the maximum current passing through the inductor is $[0.584 \mathrm{A}]$

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

University of Washington

Hope College

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.

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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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but this problem we haven't l c circuit. The capacitors initially charged up to 16 bolts, and we have a capacitance of five micro fair reds and induct INTs of 3.75 million Aires. First part is toe calculate the total stored energy. So to do this, we're gonna recall that the stored energy on a capacitor is given by 1/2 the charge. What's fine by whatever the voltage differences between the two plates can also rewrite this by recalling that the charges given by our capacitance multiply buyer voltage. So first we could replace the queue to get 1/2 C v squared. Or we could replace the voltage. And this is Q squared over to see here will have our total stored energy when that voltage difference across the capacitor plates is that maximum value is what it's charged up to about 16 bolts. So if we know the voltage difference and we know the capacitance, the relevant equation here is gonna be this guy. Sorry, you max. 1/2 C V squared 1/2 five micro Farage's And then that maximum voltage Our max about that here is 16 squared. It gets a 6.4 times 10. Did the negative four jewels put Barbie? We want to know what the maximum current is. So to do this will want a first recall that the stored energy and a capacity here is 1/2 l I squared. So if the current is maximum, we see that the stored energy in the induct er is gonna be a maximum. It will be that value that we calculated in a So this means that are you, Max equals 1/2 0 I max Square Solving this for the maximum current we have Max equals the square root of to you. Max over are inducted. We have these two so that it is too 6.4 times 10 to the negative for Jules and then 3.75 times 10 to make it three. Miss Kitt says 0.584 amps. For the last part. We want to know what the charges on the capacitor plates from the current is maximum. But we just utilize the fact that when the current is maximum, the stored energy and the in dr is a maximum meaning that the stored energy in the capacitor is zero All of that energy is stored in the induct er when the current is a maximum. So the relevant equation here that we want to use is this last guy. So if we know that the stored energy in the capacitor zero and that's also you go to the charge of the capacitor squared over two times the capacitance, this means that the charge on the plates must be zero.

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