Problem

(a) At what frequency must the circuit in Problem…

05:18

Problem 24 Easy Difficulty

A 50.0-Hz generator with an rms voltage of 115 V is connected in series to a 3.12 -k\Omega resistor and a $1.65-\mu$ F capacitor. Find (a) the
rms current in the circuit and (b) the phase angle, $\phi$ , between the
current and the voltage.

Answer

a) 31.35 $\mathrm{mA}$
b) $31.73^{\circ}$

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Physics 102 Electricity and Magnetism

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Video Transcript

to complete the current. We begin by using a modified version off Alms Law, which is the following are amassed. His ego's too wide are a mass times the impedance. These is the alms wall for RC circuits and you want to know the IRA mess. So we solve for I R A Mass. And by doing that we get That I remember is the Coast V ROMs reminded by Z and then we have to couple it. What is easy diseases? Impedance, which is given by the square root off the resistance squared plus the reactor's squared on the reactors is two pi times the frequency times the capacitance under one. This is all squared and under the square root. Now putting it all together we get that I are a mess. Is it close to the square root off tree 0.12 key glow homes squared plus to buy times the frequency times the capacitance, which is 1.55 me crew for its This is all under one on squared and now under describe it. Finally, this is all under the voltage 115 and then by solving this calculation, we get that the R. M s current is approximately 0.0 31 35 m peers, which we can, right as 31 points, 35 Millie amperes to complete the difference off fees we use. The fact that the co sign off the fees is equals two. There is a distance divided by impedance, so it is equals. True in the square, root off R squared plus one divided by two pi FC squared all under the square root, now under the resistance, then plugging in the values given by the problem. We get that the co sign of the phase is equals. Two 3.12 times tend to the turn to buy. I did, but square root off three points. 12 times tend toward squared, plus to pie times 15 times 1.65 Time Stand to the minus six under one squared. Finally, the co sign of the phase is approximately zero point 851 and then the Ark coast Hein, off 0.851 is approximately 31 0.68 degrees

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