Chapter 24 Alternating-Current Circuit, Study notes of Electrical Circuit Analysis

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Chapter 24

Alternating

Current Circuit

Chapter

Alternating-Current Circuit

Outline 24-

Alternating Voltage and Circuit

Alternating Voltage and Circuit

In an alternating circuit, the magnitude and direction of the voltageand current change periodically, and they are a function of time:The current and voltage is the so-called alternating current (AC) andvoltage, respectively.

Figure 24-

An AC Generator Connected to a

LampLamp

Root Mean Square (rms) ValueBoth alternating voltage and current have a zero value. So directaverage gives no information (or useless).I

d

t

l

t

lt

ti

t

i

tit

In order to evaluate an alternating parameter in quantity, we useroot mean square (rms):We square the alternating current IWe square the alternating current I,

t

I

I

ω

2

2

2

sin

max

=

Now, we can average

I

2

2

2

1

)

(

I

I

2

2

max

2

)

(

I

I

av

=

RMS is square root of the above eq.,

max

2

1

I

I

rms

=

Any quantity x that varies with time as

x=x

max

sin

t

, or

Rms:

Square,

average, square root

x=x

max

cos

t, obey the relationships:

RMS Value of a Quantity with Sinusoid Time DependenceRMS

Value of a Quantity with Sinusoid Time Dependence

(^2) max

2

x

x

av

max max

x

x

rms

av

So, the rms value of the voltage in a AC circuit is

V

V

max

V

V

rms

Also suitable for current!

Solution

max

V

V

rms

Since

, we have

The maximum and peak is:

V

V

V

V

max

rms

V

V

V

V

“Average” Power

Since

P = I

2

R

Replace

I

with

I

we have the average value of P

Replace

I

with

I

rms

, we have the average value of P

R

I

P

rms

av

2

=

2

V

Apply Ohm’s law,

)

6

24

(

−

=

R

V

P

rms

av

Rms can operate directly for Ohm law!

Solution(a) The rms voltage is

V

V

V

rms

max

rms

max

(b) The rms current is

V

V

rms

rms

V

V

I

A

R

(c) The average power(c)

The average power

W

V

R

V

P

rms

av

2

2

R

(d) The maximum power

2

2

W W R V R V P

rms

2

max 2

max

×

Homework

Problems: 2,

2. In many European homes the rms voltage available

from a wall socket is 240 V. What is the maximumvoltage in this case?

4. The rms current in an ac circuit with a resistance of 150 Ω

is 0.85 A. What are the (a) average and (b) maximum

power consumed by this circuit?

SS

ummary

The calculate of RMS for a

x=x

max

sin

ω

t

,

or

x=x

max

cos

ω

t

function