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When an ac generator with a frequency of 180 $\mathrm{Hz}$ and an rmsvoltage of 36 $\mathrm{V}$ is connected to an $R C$ circuit, the rms current is0.28 $\mathrm{A}$ . If the resistance has a value of $54 \Omega,$ what is the value ofthe capacitance?

7.6$\mu \mathrm{F}$

Physics 102 Electricity and Magnetism

Chapter 24

Alternating-Current Circuits

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Alternating Current

University of Washington

Hope College

University of Winnipeg

McMaster University

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we begin this question by calculating the impudence off the circuit so we can couple of impudence by using and adapted for off homes low. Which is the r a mass is he goes to Why we mass times p this so I didn't do this. These equals two V hurry mass divided by I are a mess which using the information given in the problem. Zico Stoop 36 divided by 0.28. And now we remember that the students is given by the square root off the resistance squared plus and the reactor squared where the reactant is given by one divided by two pie factory frequency times the capacitors squared so we can solve for the capacitance To get Z squared, he's equals towards squared Plus to buy FC under one squared. No, we have one Divided by two pi embassy is equal to the square. Root off these words. Minds are squared Then to buy F seat is equals to one divided by the square root off Z squared minus R squared And finally the capacitance is given by to pi times the frequency times the square it off the squared minds are squared this is all under one and now blinking all the values even by the problem on our impudence, we get that the capacitance is the question to pie times 180 times the square root off 36 divided by 0.28 squared, minus 54 squired. This is all in the war, then, is approximately 7.6 times 10 to the minus six for us and 10 for the minor. Six was on my crew then the capacitance is approximately 7.6 me crow forest.

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