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RC RC Circuits Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems DC/AC Fundamentals: A Systems Approach Approach

RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

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Page 1: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

RCRC Circuits Circuits

Chapter 10

Thomas L. Floyd

David M. Buchla

DC/AC Fundamentals: A Systems DC/AC Fundamentals: A Systems ApproachApproach

Page 2: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

When resistance and capacitance are connected in series, the phase angle between the applied voltage and total current is between 0 and 90, depending on the values of resistance and reactance.

Ch.10 Summary

Sinusoidal Response of RC Circuits

R C

VS

VR leads VS

VSVR

VC lags VS

VS VC

I

I leads VS

VS

Page 3: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

In a series RC circuit, the total impedance is the phasor sum of R and XC.

R is plotted along the positive x-axis.

XC is plotted along the negative y-axis.

It is convenient to reposition the phasors so they form an impedance triangle.

Z is the diagonal

Ch.10 Summary

Impedance of Series RC Circuits

R

XC1tan

R

Z

R

Z

XCXC

Page 4: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Sketch the impedance triangle and show the values for R = 1.2 k and XC = 960 .

Ch.10 Summary

Impedance of Series RC Circuits

kΩ 1.33kΩ (0.96kΩ (1.2 2222 CXRZ

39

kΩ 1.2

kΩ 0.96tan

tan

1

1

R

XC

Z = 1.33 kXC = 960

R = 1.2 k

39o

Page 5: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Ohm’s law is applied to series RC circuits using Z, V, and I.

Because I is the same everywhere in a series circuit, you can obtain the various component voltages by multiplying the impedance of that component by the current, as the following example demonstrates.

Ch.10 Summary

Series RC Circuit Analysis

I

V Z

Z

V I IZV

Page 6: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Assume the current in the previous example is 10 mA. Sketch the voltage phasor diagram. (The impedance triangle from the previous example is shown for reference.)

The voltage phasor diagram can be found using Ohm’s law. Multiply each impedance phasor by 10 mA (as shown below):

Ch.10 Summary

Series RC Circuit Analysis

x 10 mA =

Z = 1.33 kXC = 960

R = 1.2 k

39o 39o

VR = 12 V

VC = 9.6 VVS = 13.3 V

Page 7: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Reactance phasors can only be drawn for a single frequency because X is a function of frequency.

Ch.10 Summary

Phase Angle vs. Frequency

As frequency changes, the impedance triangle for an RC circuit changes as illustrated here because XC decreases with increasing f. This determines the frequency response of RC circuits.

Z3

XC1

XC2

XC3

Z2

1

2

f

f

f

3

R Increasing f

3

2

1

Z1

Page 8: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

A series RC circuit can be used to produce a phase lag by a specific amount between an input voltage and an output by taking the output across the capacitor. This circuit is a basic low-pass filter, a circuit that passes low frequencies and rejects all others. This filter passes low frequencies up to a frequency called the cutoff frequency.

Ch.10 Summary

Application

(phase lag)

(phase lag)

V

Vin Vout

VinVout

VR

ff

Page 9: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Reversing the components in the previous circuit produces a circuit that is a basic lead network. This circuit is a basic high-pass filter, a circuit that passes high frequencies and rejects all others. This filter passes high frequencies down to a frequency called the cutoff frequency.

Ch.10 Summary

Application

(phase lead)

V

R(phase lead)

VinVout

Vout

VinVC

Vout

Vin

Page 10: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

An application showing how a phase-shift network is useful is the phase-shift oscillator, which uses a combination of RC networks to produce a 180o phase shift that is required for the oscillator to work.

Ch.10 Summary

Application

Amplifier

R R R

C C CPhase-shift network

Rf

Page 11: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

For parallel circuits, it is useful to introduce two new quantities (susceptance and admittance) and to review conductance.

Ch.10 Summary

AC Response of Parallel RC Circuits

Conductance is the reciprocal of resistance. R

G1

Capacitive susceptance is the reciprocal of capacitive reactance. C

C XB

1

Admittance is the reciprocal of impedance.Z

Y1

Page 12: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

In a parallel RC circuit, the admittance phasor is the sum of the conductance and capacitive susceptance phasors:

From the diagram, the phase angle is:

Ch.10 Summary

AC Response of Parallel RC Circuits

22CBGY

VS G BCBC Y

G

G

BC1tan

Page 13: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Draw the admittance phasor diagram for the circuit.

The magnitudes of conductance, susceptance, and admittance are:

Ch.10 Summary

AC Response of Parallel RC Circuits

mS 1kΩ 1

11

RG mS 628μF) kHz)(.01 (102

1

CC X

B

mS 1.18mS) (0.628mS) (1 2222 BGY C

VSR C

f =10 kHz

1 k 0.01 mFY

G = 1 mS

BC

628 mS1.18 mS

Page 14: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Ohm’s law can be applied to parallel RC circuits using Y, V, and I.

Because V is the same across all components in a parallel circuit, you can obtain the current in a given component by simply multiplying the admittance of the component by the voltage, as illustrated in the following example.

Ch.10 Summary

Analysis of Parallel RC Circuits

V

IY VYI

Y

IV

Page 15: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

If the voltage in the previous example is 10 V, sketch the current phasor diagram. The admittance diagram from the previous example is shown below for reference.

The current phasor diagram can be found from Ohm’s law. Multiply each admittance phasor by 10 V.

Ch.10 Summary

Analysis of Parallel RC Circuits

x 10 V=

x 10 V=Y =

1.18 mS

G = 1.0 mS

BC = 0.628 mS

IR = 10 mA

IC = 6.28 mA

IS = 11.8 mA

Page 16: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Notice that the formula for capacitive susceptance is the reciprocal of capacitive reactance. Thus BC and IC are directly proportional to f:

Ch.10 Summary

Phase Angle of Parallel RC Circuits

fCBC 2

As frequency increases, BC and IC must also increase, so the angle between IR and IS must increase.

IC IS

IR

Page 17: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

For every parallel RC circuit there is an equivalent series RC circuit at a given frequency. The equivalent resistance and capacitive reactance are shown on the impedance triangle:

Ch.10 Summary

Equivalent Series and Parallel RC Circuits

Z

Req = Z cos

XC(eq) = Z sin

Page 18: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Series-parallel RC circuits are combinations of both series and parallel elements. These circuits can be solved by methods from series and parallel circuits.

The total impedance can be found by converting the parallel components to an equivalent series combination, then adding the result to R1 and XC1 to get the total reactance.

The components in the yellow box are in parallel:

Ch.10 Summary

Series-Parallel RC Circuits

R C

R2 C2

Z1

R1 C1

R2 C2

Z2

21

211 CXRZ

22

22

222

C

C

XR

XRZ

For example, the components in the green box are in series:

Page 19: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

An oscilloscope is commonly used to measure phase angle in reactive circuits. The easiest way to measure phase angle is to set up the two signals to have the same apparent amplitude and measure the period. An example of a Multisim simulation is shown, but the technique is the same in lab.

Set up the oscilloscope so that two waves appear to have the same amplitude as shown.

Determine the period. For the wave shown, the period is

Ch.10 Summary

Measuring Phase Angle

μs 160div

μs 20div) (8.0

T

Page 20: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Next, spread the waves out using the SEC/DIV control in order to make an accurate measurement of the time difference between the waves. In the case illustrated, the time difference is

The phase shift is calculated from

55o

Ch.10 Summary

Measuring Phase Angle (Cont’d)

μs 24.5div

μs 5div) (4.9

t

360

μs 160

μs 24.5360

T

Δt

Page 21: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

As shown earlier, you can multiply the impedance phasors for a series RC circuit by the current to obtain the voltage phasors. The earlier example is shown below for review:

Ch.10 Summary

The Power Triangle

x 10 mA =

Z = 1.33 kXC = 960

R = 1.2 k

39o 39o

VR = 12 V

VC = 9.6 VVS = 13.3 V

Multiplying each value in the left-hand triangle gives you the corresponding value in the right-hand triangle.

Page 22: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Multiplying the voltage phasors by Irms (10 mA) gives the power triangle values (because P = VI ). Apparent power is the product of the magnitude of the current and magnitude of the voltage and is plotted along the hypotenuse of the power triangle.

Ch.10 Summary

The Power Triangle (Cont’d)

VR = 12 V

VS = 13.3 V

VC = 9.6 V

x 10 mA=

x 10 mA=

x 10 mA=

Ptrue = 120 mW

Pa = 133 mVA

Pr = 96 mVAR

Page 23: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Power factor is the ratio of true power (in W) to apparent power (in VA). Volt-amperes multiplied by the power factor equals true power. Power factor can be determined using:

Power factor can vary from 0 (for a purely reactive circuit) to 1 (for a purely resistive circuit).

Ch.10 Summary

Power Factor

PF cos

Page 24: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Apparent power consists of two components; the true power component, which does the work, and a reactive power component, that is simply power shuttled back and forth between source and load.

Ch.10 Summary

Apparent Power

Some components such as transformers, motors, and generators are rated in VA rather than watts.

Ptrue (W)

Pa (VA)

Pr (VAR)

Page 25: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

10 V dc

VoutVin

100

1 Fm10 V dc

0

10 V dc

0

When a signal is applied to an RC circuit, and the output is taken across the capacitor as shown, the circuit acts as a low-pass filter.

As the frequency increases, the output amplitude decreases.

Plotting the response:

1ƒ = 1 kHz

8.46 V rms10 V rms 100

Fm1.57 V rms

10 V rms

1ƒ = 10 kHz100

Fm0.79 V rms

10 V rms

1ƒ = 20 kHz

100

Fm

Ch.10 Summary

RC Circuit Frequency Response

Vout (V)

9.98

8.46

1.570.79

0.1 1 10 20 100f (kHz)

9

8

7

6

5

4

3

2

1

Vout (V)

9.98

8.46

1.570.79

0.1 1 10 20 100f (kHz)

9

8

7

6

5

4

3

2

1

Page 26: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Vin

10 V dc

0

Vout

0 V dc10 V dc 100 1 Fm

Reversing the components, and taking the output across the resistor as shown, the circuit acts as a high-pass filter.

As the frequency increases, the output amplitude also increases.

Plotting the response:

ƒ = 100 Hz

0.63 V rms10 V rms

100 1 Fm

ƒ = 1 kHz

5.32 V rms10 V rms

100 1 Fm

ƒ = 10 kHz

9.87 V rms10 V rms

100 1 Fm

Ch.10 Summary

RC Circuit Frequency Response

Vout (V)

f (kHz)

9.87

5.32

0.6300.01 0.1 1

10

9

8

7

6

5

4

3

2

1

10

Vout (V)

f (kHz)

9.87

5.32

0.63

00.01 0.1 1

10

9

8

7

6

5

4

3

2

1

10

Page 27: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

The total opposition to sinusoidal current expressed in ohms.

The ability of a capacitor to permit current; the reciprocal of capacitive reactance, measured in siemens (S).

The angle between the source voltage and the total current in a reactive circuit.

A measure of the ability of a reactive circuit to permit current; the reciprocal of impedance, measured in siemens (S).

Ch.10 Summary

Key TermsImpedance

Phase angle

Capacitive susceptance

(BC)

Admittance (Y)

Page 28: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

The frequency at which the output voltage of a filter is 70.7% of the maximum output voltage.

In electric circuits, the variation of the output voltage (or current) over a specified range of frequencies.

The relationship between volt-amperes and true power or watts. Volt-amperes multiplied by the power factor equals true power.

Ch.10 Summary

Key Terms

Power factor

Frequency response

Cutoff frequency

Page 29: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

1. If you know what the impedance phasor diagram looks like in a series RC circuit, you can find the voltage phasor diagram by

a. multiplying each phasor by the current

b. multiplying each phasor by the source

voltage

c. dividing each phasor by the source voltage

d. dividing each phasor by the current

Ch.10 Summary

Quiz

Page 30: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

2. A series RC circuit is driven with a sine wave. If the output voltage is taken across the resistor, the output will

a. be in phase with the input.

b. lead the input voltage.

c. lag the input voltage.

d. none of the above

Ch.10 Summary

Quiz

Page 31: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

3. A series RC circuit is driven with a sine wave. If you measure 7.07 V across the capacitor and 7.07 V across the resistor, the voltage across both components is

a. 0 V

b. 5 V

c. 10 V

d. 14.1 V

Ch.10 Summary

Quiz

Page 32: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

4. If you increase the frequency in a series RC circuit,

a. the total impedance will increase

b. the reactance will not change

c. the phase angle will decrease

d. none of the above

Ch.10 Summary

Quiz

Page 33: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

5. Admittance is the reciprocal of

a. reactance

b. resistance

c. conductance

d. impedance

Ch.10 Summary

Quiz

Page 34: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

6. Given the admittance phasor diagram of a parallel RC circuit, you could obtain the current phasor diagram by

a. multiplying each phasor by the voltage

b. multiplying each phasor by the total current

c. dividing each phasor by the voltage

d. dividing each phasor by the total current

Ch.10 Summary

Quiz

Page 35: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

7. If you increase the frequency in a parallel RC circuit,

a. the total admittance will decrease

b. the total current will not change

c. the phase angle between IR and IS will

decrease

d. none of the above

Ch.10 Summary

Quiz

Page 36: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

8. The magnitude of the admittance in a parallel RC circuit will be larger if

a. the resistance is larger

b. the capacitance is larger

c. both a and b

d. none of the above

Ch.10 Summary

Quiz

Page 37: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

9. The maximum power factor occurs when the phase angle is

a. 0o

b. 30o

c. 45o

d. 90o

Ch.10 Summary

Quiz

Page 38: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

10. When power is calculated from voltage and current for an ac circuit, the voltage and current should be expressed as

a. average values

b. rms values

c. peak values

d. peak-to-peak values

Ch.10 Summary

Quiz

Page 39: RC Circuits Chapter 10 Thomas L. Floyd David M. Buchla DC/AC Fundamentals: A Systems Approach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

1. a

2. b

3. c

4. c

5. d

6. a

7. d

8. d

9. a

10. b

Ch.10 Summary

Answers