Ch 35 Physics for Scientists and Engineers

Ch 35 Physics for Scientists and Engineers - AC CIRCUITS...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
AC CIRCUITS 35.1. Model: Solve: A phasor is a vector that rotates counterclockwise around the origin at angular frequency w. (a) Refemng to the phasor in Figure Ex35.1, the phase angle is 2*618 rad = 175 rad / s n rad 180" 15~10~~ s U? = 180' - 30" = 150° x - = 2.618 rad w = (b) The instantaneous value of the emf is & = €, cosw = (10 V)cos(2.618 rad) = -8.66 V Be careful to change your calculator to the radian mode to work with the trigonometric functions. Assess: 35.2. Model: Solve: A phasor is a vector that rotates counterclockwise around the origin at angular frequency (a) Refemng to the phasor in Figure Ex35.2, the phase angle is (b) From Figure Ex35.2, = 70.7 v & cos on &=€ocosw*€o =-= cos( ~t 1 4 rad) 35.3. Model: Solve: The emf is A phasor is a vector that rotates counterclockwise around the origin at angular velocity w. E=&,coswt = (50 V)cos(2a x 11 1 rads x 3.0 x s) = (50 V)cos(2.092 rad) = (50 V)cos120° Phasor at f = 3.0 rns 35.4. Model: Solve: A phasor is a vector that rotates counterclockwise around the origin at angular velocity w. The instantaneous emf is given by the equation &= (170 V) COS[(?I~X 60 Hz)t] At i = 60 ms, E= (170 V) cos (22.619 rad). An angle of 22.619 rad corresponds to 3.60 periods, which implies that the phasor makes an angle of (0.60)2a rad or (0.60)(360") = 2 16" in its fourth cycle. 35-1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
35-2 Chapter 35 Phah at f=60ms 35.5. Solve: Visualize: Please refer to Figure 35.4 for an AC resistor circuit. (a) For a circuit with a single resistor, the peak current is (b) The peak current is the same as in part (a) because the current is independent of frequency. 35.6. frequency w. Visualize: Solve: Model: Current and voltage phasors are vectors that rotate counterclockwise around the origin at angular Please refer to Figure (a) From the figure we note that V, = 10 V and I, = 0.50 A. Using Ohm's law, The frequency is 01 1 28 T 0.04 s f =-=-=-- - 25 Hz (c) The voltage and current are vR = VR COSW = (10 V)cos[2~(25 Hz)t] For both the voltage and the current at t = 15 ms, the phase angle is i, = IR COS@ = (0.50 A)cos[2~(25 Hz)~] ux = 2d25 Hz)(15 ms) = 2N0.375) rad = 135" That is, the current and voltage phasors will make an angle of 135" with the starting t = 0 s position. I S='O" ' ql=;.50A I I v\ 0 I Assess: and voltage are in phase. law applies to both the instantaneous and peak currents and voltages. For a resistor, the current
Background image of page 2
AC Circuits 35-3 35.7. Visualize: Figure 35.7 shows a simple one-capacitor circuit. Solve: (a) The capacitive reactance at o= 2@= 2n(lOO Hz) = 628.3 rad/s is = 5305 R 1 1 x,=-= WC (628.3 rad / s)(0.30 x 10" F) 10.0 v ,,=E= =1.88~10-~ A=1.88mA X, 5.305~10~ C2 (b) The capacitive reactance at [email protected] kHz) = 628,300 rad/s is 1 1 x, =-= = 5.305 R (6.283 x lo5 rad / s)(0.30 x lo4 F) Assess: increase in w , as observed above. Using reactance is just like using resistance in Ohm's law. Because Xc = w-', decreases' with an 35.8. Solve: (a) For a simple one-capacitor circuit, When the frequency is doubled, the new current is I; = W'CV, = (2W)CVC = 2(WCv,) = 21, = 20.0 mA (b) Likewise, when the voltage is doubled, the current doubles to 20.0 mA. (c) When the frequency is halved and the emf is doubled, the current remains the same at 10.0 mA.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This homework help was uploaded on 04/07/2008 for the course PHSX 211/212 taught by Professor Medvedev during the Spring '08 term at Kansas.

Page1 / 22

Ch 35 Physics for Scientists and Engineers - AC CIRCUITS...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online