Chapter 14: Problem 20
Discuss possible practical applications of \(R L\) circuits.
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Chapter 14: Problem 20
Discuss possible practical applications of \(R L\) circuits.
These are the key concepts you need to understand to accurately answer the question.
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In an oscillating \(\quad R L C \quad\) circuit, \(R=7.0 \Omega, L=10 \mathrm{mH},\) and \(C=3.0 \mu \mathrm{F} .\) Initially, the capacitor has a charge of \(8.0 \mu \mathrm{C}\) and the current is zero. Calculate the charge on the capacitor (a) five cycles later and (b) 50 cycles later.
In an oscillating \(R L C\) \(R=5.0 \Omega, L=5.0 \mathrm{mH},\) and \(C=500 \mu \mathrm{F} .\) What is the angular frequency of the oscillations?
A rectangular copper ring, of mass \(100 g \) and resistance \(0.2 \Omega,\) is in a region of uniform magnetic field that is perpendicular to the area enclosed by the ring and horizontal to Earth's surface. The ring is let go from rest when it is at the edge of the nonzero magnetic field region (see below). (a) Find its speed when the ring just exits the region of uniform magnetic field. (b) If it was let go at \(t=0,\) what is the time when it exits the region of magnetic field for the following values:\(a=25 \mathrm{cm}, b=50 \mathrm{cm}, B=3 \mathrm{T},\) and \(\quad g=9.8 \mathrm{m} / \mathrm{s}^{2} ?\) Assume the magnetic field of the induced current is negligible compared to \(3 T\).
A \(10-\mathrm{H}\) inductor carries a current of \(20 \mathrm{A}\). How much ice at \(0^{\circ} \mathrm{C}\) could be melted by the energy stored in the magnetic field of the inductor? (Hint: Use the value \(L_{\mathrm{f}}=334 \mathrm{J} / \mathrm{g}\) for ice.)
Two coils close to each other have a mutual inductance of \(32 \mathrm{mH} .\) If the current in one coil decays according to \(I=I_{0} e^{-\alpha t},\) where \(I_{0}=5.0 \mathrm{A}\) and \(\alpha=2.0 \times 10^{3} \mathrm{s}^{-1}\) what is the emf induced in the second coil immediately after the current starts to decay? At \(t=1.0 \times 10^{-3} \mathrm{s} ?\)
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