Ohm\'s Law notes that the resistance of a resistor is equal to the ratio of the

Question

Ohm's Law notes that the resistance of a resistor is equal to the ratio of the resistor's peak voltage over its peak current: In Investigation #3. you learned that a similar relationship holds for a capacitor The capacitive reactance is equal to the ratio of the capacitor's peak voltage over its peak current In an RC circuit, the ratio of the peak source voltage over the peak current is called the impedance and is symbolized with the letter Z; Write an expression for the impedance. Z. in terms of the resistance. R. and the capacitive reactance. Xc Write an expression for the impedance, Z. in terms of the resistance. R, the capacitance. C, and the angular frequency, omega . Hint: wrote an expression for the capacitance reactance. Xc, in question Q3T.19. Z = Let the symbol theta represent the phase difference between voltage across the source and the current thru it. Label the phase difference. theta, in the phasor diagram on the previous Does the current thru the source lead or trail the voltage across the source? Notice that the phase difference. theta, is one of the angles of a right triangle. Use the arctangent function to write an expression for the phase difference. theta, in terms of the peak voltage across the resistor. VR, and the peak voltage across the capacitor. Vc, Rewrite your expression for the phase angle. 0. so that it is expressed in terms of the resistance. R, and the capacitive reactance, Xc Finally, rewrite your expression for the phase angle. theta, so that it is expressed in terms of the resistance, R, the capacitance. C, and the angular frequency, omega. Capacitance is defined as the ratio capacitor over the voltage across the capacitor: One way of imagining a purely rest two plates of the capacitor are prove they touch (i e . the capacitor become What is the voltage across the capacitor when its plates touch? if the charge on each plate of the e capacitor Qc V stave circuit is to imagine that the cd closer and closer together until becomes a wire). What is the capacitance of the capacitor when its plates touch? When C . write expressions for: the impedance. Z. die phase difference. theta, Discuss whether the expressions you wrote in the previous question agree with what you would expect in a purely resistive circuit. When R = 0. write expressions for the impedance. Z, the phase difference. theta, Discuss whether the expressions you wrote in the previous question agree with what you would expect in a purely capacitive circuit.

Explanation / Answer

1. impedence Z^2 = R^2 +XC^2

where XC = capacitive reactance = 1/(2pifC)

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2. Current is RLC ckt will lead the volatge

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3. theta = Vl-Vc/R

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4. Theta = -Xc/R

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5. theta = Xl-XC/R or XL-(1/2pifC)/R

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6. Vacross Capaciatnce Vc =i XC

where i = V/Z

capacitanceC = (1/2pifXc)

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7. Z^2 =   XC^2

Z   = XC = 1/2pifC)

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8 phase angle tan theta   = -XC/R

power factor cos theta = R/XC

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9. z^2 = xc^2+ R^2

when R = 0

Z= XC

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10. phase = tan theta = -XC/Z

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