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(a) Determine the power factor for an RC cir. cuit with $R=4.0 \mathrm{k} \Omega$ and $C=0.35 \mu \mathrm{F}$ that is connected to an acgenerator with an rms voltage of 24 $\mathrm{V}$ and a frequency of 150 $\mathrm{Hz}$ .(b) Will the power factor for this circuit increase, decrease, or staythe same if the frequency of the generator is increased? Explain.

a) $\cos \phi=0.797$b) When frequency increases the capacitive reactance decre ases$\left(\because X_{C}=\frac{1}{\omega C}=\frac{1}{2 \pi f C}\right)$As capacitive reactance decreases the impedance of the circuit decreases$\left(Z=\sqrt{R^{2}+X_{c}^{2}}\right)$

Physics 102 Electricity and Magnetism

Chapter 24

Alternating-Current Circuits

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

Alternating Current

Cornell University

University of Michigan - Ann Arbor

McMaster University

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the power factor is just the co sign off the face and the co sign of the phase is egos true. The resistance divided by the MP does, and these equals to this square it off r squared plus to pie F. C under one squared is all under the resistance again, so lugging their values that were given leave the problem. We get that the cool sign off. Five Zico's troop This square root four time stamped toward there is one key. Loom there squared plus two pi times the frequency 115 times the capacitance 0.25 meat group under one squared square root. This is all under the resistance four times stand to deterred. Finally, disease approximately 0.797 Now we noted that the power factor is proportional the resistance inversely proportional to the impudence on DDE, The impedance is equal to the square root off r squared plus the reactant squared under the resistance again now knows that the reactant is he goes to two pi frequency capacitance under one. So you for you increase the freakin separation. Narrator So by increasing f, we will be decreasing the reactor's so we will be decreasing these factor here and by decreasing that this factor here we will be decreasing. They didn't need her as a wolf on decreasing the denominator means that the complete fraction will increase, so increasing the frequency implies that the power factor also increases.

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