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A $12.5-\mu \mathrm{F}$ capacitor and a $47.5-\mu \mathrm{F}$ capacitor are connected to an ac generator with a frequency of 60.0 $\mathrm{Hz}$ . What is the capaci-tive reactance of this pair of capacitors if they are connected (a) inparallel or ( b) in series?

a) 44.2$\Omega$b) 268$\Omega$

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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if the capacitors are connected in parallel, the privilege capacitance is given by the sam off the capacitance is and then we completing their values, given by the problem to get 12.5 plus 47.5, which years? Well, 60 Negro for its then we can now use the equation for their reactor's off. The capacitor, which is given by X, is equal to one divided by two pi times the frequency times the capacitance off that equivalent capacitor, and these is equals to one divided by two pi Time. 60 times 60 again thanks 10 to the minus six because of his micro here and these is approximately 44 0.2 owns. No. If we had, we connected the capacitors in Syria's. Instead, the equivalent capacitance will be given by one over CR. It's equals to one. Oversee one plus one movers, too. Then one oversee our is equals to see one plus c two divided by C one times two. Finally, the equivalent capacitance is equals two C one time see two divided by C one policy too. And then we get the following result. So the equivalent capacitance is equals two 12.5 times 47.5 times, then to the minus 12 minus 12. Because there is a minor six from these micro and another minor six from this microbe and these is divided by 60 times, 10 to the minus six. Then the equivalent capacitance is he goes to 12.5 times 47.5. I understand to the money. Six. Divided by 60. No, we complex the reactor's X. Here is he close to one. Divided by two pi times 60 times 12.5 times 47.5 Time Stand for the mind six Divided by 60 Simplify here and we get approximately 268 homes.

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