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Suppose we would like to change the phase angle for this circuit to $\phi=-25.0^{\circ},$ andwe would like to accomplish this by changing the resistor to avalue other than 175$\Omega$ . The inductor is still 90.0 $\mathrm{mH}$ , the capacitor is 15.0$\mu \mathrm{F}$ , the rms voltage is $120.0 \mathrm{V},$ and the ac frequencyis 60.0 $\mathrm{Hz}$ . (a) Should the resistance be increased or decreased?Explain. (b) Find the resistance that gives the desired phase angle. (c) What is the rms current in the circuit with the resistance foundin part (b)?

a) See explanationb) see workc) 0.354 $\mathrm{A}$

Physics 102 Electricity and Magnetism

Chapter 24

Alternating-Current Circuits

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Alternating Current

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on the first item. Remember that the faith and hope the tangent of the face and gold is equals two eggs l minus x c divided by the resistance before changing anything in the circuit. Their value off the face is my news. 35.3 degrees. By drawing the geometric cycle here, we can sketch attention off minus 35.3 as being somewhere down here we want to change the things and go toe minus 25. When doing that the new tangent, we will be somewhere this please. So what happens here is that the value off the ancient is getting closer to zero. In order to do that by looking at the expression for the tensions of the face and we see that we have to increase the resistance since both they looked in on the capacitance are still the same on the second item, we now have to calculate what is the value off that new resistance to do So we remember we use this equation that we have just mentions for the tangent of the face on. So the tangent off the new face on go minus 25 degrees is equals two eggs. L'm I know. Zach. See, 33.9. Mine was 177 divided by your value off the new resistance. Then the value of the new resistance is a close to 33.9 miners 177 divided by the tangent off minus 25 degrees. And this is approximately tree 07 homes on the last item. We have to calculate the value off the current after changing the resistance. So we remember on floor B R. A mass is in Costa. Why are a mass times didn't see this? And so for the current to get your a mass is equals to be are a mass divided by Z We still the same. So the only thing that changes is the impedance and we get the current eyes. Uh, 120. Divided by the square root off R squared New resistance squared plus excel miners exceed 33.9 miners 177 squared, which gives us a current off approximately 0.354 amperes

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