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# Alternating Current Mcqs(Set -1) And Theory NEET Notes | EduRev

## NEET : Alternating Current Mcqs(Set -1) And Theory NEET Notes | EduRev

``` Page 1

Physics Including Human Applications

554
Chapter 25
Alternating Currents

GOALS
When you have mastered the contents of this chapter, you will be able to achieve the
following goals:
Definitions
Define each of the following terms and use it in an operational definition:
effective values of current and voltage
reactance
impedance
power factor
resonance
Q-factor
AC Circuits
Solve alternating-current problems involving resistance, inductance, and capacitance in
a series circuit.
Phasor Diagrams
Draw phasor diagrams for alternating current circuits.
Transformer
Explain the operation of the transformer.
AC Measurements
Describe the use of alternating currents in physiological measurements.

PREREQUISITES
Before you begin this chapter you should have achieved the goals of Chapter 22, Basic
Electrical Measurements, and Chapter 24, Electromagnetic Induction.
Page 2

Physics Including Human Applications

554
Chapter 25
Alternating Currents

GOALS
When you have mastered the contents of this chapter, you will be able to achieve the
following goals:
Definitions
Define each of the following terms and use it in an operational definition:
effective values of current and voltage
reactance
impedance
power factor
resonance
Q-factor
AC Circuits
Solve alternating-current problems involving resistance, inductance, and capacitance in
a series circuit.
Phasor Diagrams
Draw phasor diagrams for alternating current circuits.
Transformer
Explain the operation of the transformer.
AC Measurements
Describe the use of alternating currents in physiological measurements.

PREREQUISITES
Before you begin this chapter you should have achieved the goals of Chapter 22, Basic
Electrical Measurements, and Chapter 24, Electromagnetic Induction.
Physics Including Human Applications

555
Chapter 25
Alternating Currents

25.1 Introduction
Most of your experience with electricity has probably been with alternating current
(AC) circuits. Do you know the difference between AC and direct current (DC)
electricity? At some time or another you have probably read the printing on the end of a
light bulb. Usually a light bulb has printed on it that it is for use in a 120-volt AC circuit.
What was the manufacturer trying to indicate? Could you use a 120-V DC bulb in your
household sockets? What, if anything, would happen? Why is AC the dominant form of
electrical energy in use? More than 90 percent of electrical energy is used as AC
electricity.
If you owned an electric train in your childhood, you may recall that you used a
transformer to reduce household voltage to the voltage required by the electric train.
The transformer is a device that plays a most important role in the use of electrical
energy. Do you know what its functions are in transmission of electric power? What is
the role of the transformer in the coupling of two AC circuits? These are a few of the
questions we will discuss in this chapter.

25.2 Nomenclature Used for Alternating Currents
In Chapter 24, we learned that a simple AC generator can be made by rotating a coil of
conducting wire in a constant magnetic field. The voltage produced by such a generator
has the form shown in Figure 25.1. This sinusoidal voltage alternates polarity + to -and
produces an alternating current in a circuit connected to such an AC source. This
alternating polarity is in contrast to the unindirectional nature of DC current.

In the United States the standard frequency in home and industrial use is 60
cycles/second (Hz). This means that there is a reversal of the direction of the current
every 1/120 second. Radio broadcast frequencies are of the order of 10
6
Hz. Some
Page 3

Physics Including Human Applications

554
Chapter 25
Alternating Currents

GOALS
When you have mastered the contents of this chapter, you will be able to achieve the
following goals:
Definitions
Define each of the following terms and use it in an operational definition:
effective values of current and voltage
reactance
impedance
power factor
resonance
Q-factor
AC Circuits
Solve alternating-current problems involving resistance, inductance, and capacitance in
a series circuit.
Phasor Diagrams
Draw phasor diagrams for alternating current circuits.
Transformer
Explain the operation of the transformer.
AC Measurements
Describe the use of alternating currents in physiological measurements.

PREREQUISITES
Before you begin this chapter you should have achieved the goals of Chapter 22, Basic
Electrical Measurements, and Chapter 24, Electromagnetic Induction.
Physics Including Human Applications

555
Chapter 25
Alternating Currents

25.1 Introduction
Most of your experience with electricity has probably been with alternating current
(AC) circuits. Do you know the difference between AC and direct current (DC)
electricity? At some time or another you have probably read the printing on the end of a
light bulb. Usually a light bulb has printed on it that it is for use in a 120-volt AC circuit.
What was the manufacturer trying to indicate? Could you use a 120-V DC bulb in your
household sockets? What, if anything, would happen? Why is AC the dominant form of
electrical energy in use? More than 90 percent of electrical energy is used as AC
electricity.
If you owned an electric train in your childhood, you may recall that you used a
transformer to reduce household voltage to the voltage required by the electric train.
The transformer is a device that plays a most important role in the use of electrical
energy. Do you know what its functions are in transmission of electric power? What is
the role of the transformer in the coupling of two AC circuits? These are a few of the
questions we will discuss in this chapter.

25.2 Nomenclature Used for Alternating Currents
In Chapter 24, we learned that a simple AC generator can be made by rotating a coil of
conducting wire in a constant magnetic field. The voltage produced by such a generator
has the form shown in Figure 25.1. This sinusoidal voltage alternates polarity + to -and
produces an alternating current in a circuit connected to such an AC source. This
alternating polarity is in contrast to the unindirectional nature of DC current.

In the United States the standard frequency in home and industrial use is 60
cycles/second (Hz). This means that there is a reversal of the direction of the current
every 1/120 second. Radio broadcast frequencies are of the order of 10
6
Hz. Some
Physics Including Human Applications

556
microwave devices have frequencies the order of 10
10
Hz. So the AC current in common
use is of relatively low frequency.
If you have two equal resistors and in one there is an AC current of 1 ampere
maximum and in the other a DC current of one ampere, would you expect the two
resistors to produce the same heat? Let us consider the situation to see what we should
expect. In the resistor with the DC current, the current is constant. In the resistor with
AC current, the current varies from 0 to 1 A in one direction and the same in the
opposite direction. You have learned that the heat produced depends upon the square
of current for a given resistor. Hence, you would have been correct if you had said that
more heat is produced by the 1-A DC current. For a varying current we would expect
the heat produced to be proportional to the average value of the square of the current.
The square root of this quantity is called effective current. That is, it is the current that
would produce the same heating effect as one ampere of DC current. Let us find the
relationship between the effective AC current and maximum AC current. The AC
current at any instant of time can be expressed as a sinusoidal function of time,
i = i
max
sin ?t           (25.1)
where i
max
is the maximum value of the current, ? is the angular frequency of the AC,
and t is the time in seconds. The square of the current will be proportional to the power
dissipated in the resistor; so
i
2
= i
2
max
sin
2
?t           (25.2)
We can draw a graph of the square of the current versus the time(Figure 25.2). The total
heating effect will be proportional to the area under the curve. You see that the curve
between p and 2p radians is exactly the same as that from 0 to p radians. So we will
need to consider only half of the total cycle. The curve for the square of the DC current
is a horizontal line represented by AB. The problem is then to find the altitude for the
rectangle with the base of p which has the same areas under the i
2
max
sin
2
?t curve. By
inspection you might say that the area under AB is about equal to the area under the
i
2
max
sin
2
?t curve if A
1
= A
2
and A
3
= A
4
. This is true if OC is equal to i
2
max
/2. You can
show this by measuring the two areas.

Page 4

Physics Including Human Applications

554
Chapter 25
Alternating Currents

GOALS
When you have mastered the contents of this chapter, you will be able to achieve the
following goals:
Definitions
Define each of the following terms and use it in an operational definition:
effective values of current and voltage
reactance
impedance
power factor
resonance
Q-factor
AC Circuits
Solve alternating-current problems involving resistance, inductance, and capacitance in
a series circuit.
Phasor Diagrams
Draw phasor diagrams for alternating current circuits.
Transformer
Explain the operation of the transformer.
AC Measurements
Describe the use of alternating currents in physiological measurements.

PREREQUISITES
Before you begin this chapter you should have achieved the goals of Chapter 22, Basic
Electrical Measurements, and Chapter 24, Electromagnetic Induction.
Physics Including Human Applications

555
Chapter 25
Alternating Currents

25.1 Introduction
Most of your experience with electricity has probably been with alternating current
(AC) circuits. Do you know the difference between AC and direct current (DC)
electricity? At some time or another you have probably read the printing on the end of a
light bulb. Usually a light bulb has printed on it that it is for use in a 120-volt AC circuit.
What was the manufacturer trying to indicate? Could you use a 120-V DC bulb in your
household sockets? What, if anything, would happen? Why is AC the dominant form of
electrical energy in use? More than 90 percent of electrical energy is used as AC
electricity.
If you owned an electric train in your childhood, you may recall that you used a
transformer to reduce household voltage to the voltage required by the electric train.
The transformer is a device that plays a most important role in the use of electrical
energy. Do you know what its functions are in transmission of electric power? What is
the role of the transformer in the coupling of two AC circuits? These are a few of the
questions we will discuss in this chapter.

25.2 Nomenclature Used for Alternating Currents
In Chapter 24, we learned that a simple AC generator can be made by rotating a coil of
conducting wire in a constant magnetic field. The voltage produced by such a generator
has the form shown in Figure 25.1. This sinusoidal voltage alternates polarity + to -and
produces an alternating current in a circuit connected to such an AC source. This
alternating polarity is in contrast to the unindirectional nature of DC current.

In the United States the standard frequency in home and industrial use is 60
cycles/second (Hz). This means that there is a reversal of the direction of the current
every 1/120 second. Radio broadcast frequencies are of the order of 10
6
Hz. Some
Physics Including Human Applications

556
microwave devices have frequencies the order of 10
10
Hz. So the AC current in common
use is of relatively low frequency.
If you have two equal resistors and in one there is an AC current of 1 ampere
maximum and in the other a DC current of one ampere, would you expect the two
resistors to produce the same heat? Let us consider the situation to see what we should
expect. In the resistor with the DC current, the current is constant. In the resistor with
AC current, the current varies from 0 to 1 A in one direction and the same in the
opposite direction. You have learned that the heat produced depends upon the square
of current for a given resistor. Hence, you would have been correct if you had said that
more heat is produced by the 1-A DC current. For a varying current we would expect
the heat produced to be proportional to the average value of the square of the current.
The square root of this quantity is called effective current. That is, it is the current that
would produce the same heating effect as one ampere of DC current. Let us find the
relationship between the effective AC current and maximum AC current. The AC
current at any instant of time can be expressed as a sinusoidal function of time,
i = i
max
sin ?t           (25.1)
where i
max
is the maximum value of the current, ? is the angular frequency of the AC,
and t is the time in seconds. The square of the current will be proportional to the power
dissipated in the resistor; so
i
2
= i
2
max
sin
2
?t           (25.2)
We can draw a graph of the square of the current versus the time(Figure 25.2). The total
heating effect will be proportional to the area under the curve. You see that the curve
between p and 2p radians is exactly the same as that from 0 to p radians. So we will
need to consider only half of the total cycle. The curve for the square of the DC current
is a horizontal line represented by AB. The problem is then to find the altitude for the
rectangle with the base of p which has the same areas under the i
2
max
sin
2
?t curve. By
inspection you might say that the area under AB is about equal to the area under the
i
2
max
sin
2
?t curve if A
1
= A
2
and A
3
= A
4
. This is true if OC is equal to i
2
max
/2. You can
show this by measuring the two areas.

Physics Including Human Applications

557
Let us use the symbol I for the effective current. We can see from Figure 25.2 that the
effective current squared is equal to one-half of i
max
squared,
I
2
= (1/2) i
2
max
(25.3)
It follows, taking the square root of both sides of Equation 25.3 that the effective current
is equal to the maximum AC current divided by the square root of two,
I = i
max
/SQR RT  = 0.707 i
max
(25.4)
The effective current is called the root mean square current. Similarly we will use E to
represent the effective emf of an AC source and V to represent the effective voltage
drop in an AC circuit:
E = E
rms
= E
max
/ SQR RT  = 0.707 E
max
(25.5)
V = V
rms
= V
max
/SQR RT  = 0.707 V
max
(25.6)
The AC meters which you use measure the V
rms
and I
rms
values of an AC circuit. If the
AC line in your home is said to be 110 V, that is the effective value of the voltage. The
maximum or peak voltage would be 110 x SQR RT  or 155 V.

25.3 Phase Relations of Current and Voltage in AC Circuits
In an AC circuit containing only resistance, the instantaneous voltage and current are
always in phase. This means they are both zero at the same time and reach their
maximum value at the same time. This is shown in Figure 25.3.

In Chapter 24 you learned that whenever the current is changing in an inductive
coil, an emf is induced. This induced emf depends upon the induction of the coil and on
the time rate of change of current. In a coil, continuously changing AC current produces
an alternating emf from self-induction. According to Lenz's law this induced emf is
opposite to the applied emf. If you neglect the resistance of the coil, the emf of the
source will just be equal to the emf of self-induction in the coil. The induced emf will
cause the current in the coil to lag behind the applied emf by one-quarter of a cycle. We
say that the current in an inductor lags the voltage by 90
o
, or that the phase of the
voltage across the inductor leads the phase of the current by 90
o
. See Figure 25.4.
Page 5

Physics Including Human Applications

554
Chapter 25
Alternating Currents

GOALS
When you have mastered the contents of this chapter, you will be able to achieve the
following goals:
Definitions
Define each of the following terms and use it in an operational definition:
effective values of current and voltage
reactance
impedance
power factor
resonance
Q-factor
AC Circuits
Solve alternating-current problems involving resistance, inductance, and capacitance in
a series circuit.
Phasor Diagrams
Draw phasor diagrams for alternating current circuits.
Transformer
Explain the operation of the transformer.
AC Measurements
Describe the use of alternating currents in physiological measurements.

PREREQUISITES
Before you begin this chapter you should have achieved the goals of Chapter 22, Basic
Electrical Measurements, and Chapter 24, Electromagnetic Induction.
Physics Including Human Applications

555
Chapter 25
Alternating Currents

25.1 Introduction
Most of your experience with electricity has probably been with alternating current
(AC) circuits. Do you know the difference between AC and direct current (DC)
electricity? At some time or another you have probably read the printing on the end of a
light bulb. Usually a light bulb has printed on it that it is for use in a 120-volt AC circuit.
What was the manufacturer trying to indicate? Could you use a 120-V DC bulb in your
household sockets? What, if anything, would happen? Why is AC the dominant form of
electrical energy in use? More than 90 percent of electrical energy is used as AC
electricity.
If you owned an electric train in your childhood, you may recall that you used a
transformer to reduce household voltage to the voltage required by the electric train.
The transformer is a device that plays a most important role in the use of electrical
energy. Do you know what its functions are in transmission of electric power? What is
the role of the transformer in the coupling of two AC circuits? These are a few of the
questions we will discuss in this chapter.

25.2 Nomenclature Used for Alternating Currents
In Chapter 24, we learned that a simple AC generator can be made by rotating a coil of
conducting wire in a constant magnetic field. The voltage produced by such a generator
has the form shown in Figure 25.1. This sinusoidal voltage alternates polarity + to -and
produces an alternating current in a circuit connected to such an AC source. This
alternating polarity is in contrast to the unindirectional nature of DC current.

In the United States the standard frequency in home and industrial use is 60
cycles/second (Hz). This means that there is a reversal of the direction of the current
every 1/120 second. Radio broadcast frequencies are of the order of 10
6
Hz. Some
Physics Including Human Applications

556
microwave devices have frequencies the order of 10
10
Hz. So the AC current in common
use is of relatively low frequency.
If you have two equal resistors and in one there is an AC current of 1 ampere
maximum and in the other a DC current of one ampere, would you expect the two
resistors to produce the same heat? Let us consider the situation to see what we should
expect. In the resistor with the DC current, the current is constant. In the resistor with
AC current, the current varies from 0 to 1 A in one direction and the same in the
opposite direction. You have learned that the heat produced depends upon the square
of current for a given resistor. Hence, you would have been correct if you had said that
more heat is produced by the 1-A DC current. For a varying current we would expect
the heat produced to be proportional to the average value of the square of the current.
The square root of this quantity is called effective current. That is, it is the current that
would produce the same heating effect as one ampere of DC current. Let us find the
relationship between the effective AC current and maximum AC current. The AC
current at any instant of time can be expressed as a sinusoidal function of time,
i = i
max
sin ?t           (25.1)
where i
max
is the maximum value of the current, ? is the angular frequency of the AC,
and t is the time in seconds. The square of the current will be proportional to the power
dissipated in the resistor; so
i
2
= i
2
max
sin
2
?t           (25.2)
We can draw a graph of the square of the current versus the time(Figure 25.2). The total
heating effect will be proportional to the area under the curve. You see that the curve
between p and 2p radians is exactly the same as that from 0 to p radians. So we will
need to consider only half of the total cycle. The curve for the square of the DC current
is a horizontal line represented by AB. The problem is then to find the altitude for the
rectangle with the base of p which has the same areas under the i
2
max
sin
2
?t curve. By
inspection you might say that the area under AB is about equal to the area under the
i
2
max
sin
2
?t curve if A
1
= A
2
and A
3
= A
4
. This is true if OC is equal to i
2
max
/2. You can
show this by measuring the two areas.

Physics Including Human Applications

557
Let us use the symbol I for the effective current. We can see from Figure 25.2 that the
effective current squared is equal to one-half of i
max
squared,
I
2
= (1/2) i
2
max
(25.3)
It follows, taking the square root of both sides of Equation 25.3 that the effective current
is equal to the maximum AC current divided by the square root of two,
I = i
max
/SQR RT  = 0.707 i
max
(25.4)
The effective current is called the root mean square current. Similarly we will use E to
represent the effective emf of an AC source and V to represent the effective voltage
drop in an AC circuit:
E = E
rms
= E
max
/ SQR RT  = 0.707 E
max
(25.5)
V = V
rms
= V
max
/SQR RT  = 0.707 V
max
(25.6)
The AC meters which you use measure the V
rms
and I
rms
values of an AC circuit. If the
AC line in your home is said to be 110 V, that is the effective value of the voltage. The
maximum or peak voltage would be 110 x SQR RT  or 155 V.

25.3 Phase Relations of Current and Voltage in AC Circuits
In an AC circuit containing only resistance, the instantaneous voltage and current are
always in phase. This means they are both zero at the same time and reach their
maximum value at the same time. This is shown in Figure 25.3.

In Chapter 24 you learned that whenever the current is changing in an inductive
coil, an emf is induced. This induced emf depends upon the induction of the coil and on
the time rate of change of current. In a coil, continuously changing AC current produces
an alternating emf from self-induction. According to Lenz's law this induced emf is
opposite to the applied emf. If you neglect the resistance of the coil, the emf of the
source will just be equal to the emf of self-induction in the coil. The induced emf will
cause the current in the coil to lag behind the applied emf by one-quarter of a cycle. We
say that the current in an inductor lags the voltage by 90
o
, or that the phase of the
voltage across the inductor leads the phase of the current by 90
o
. See Figure 25.4.
Physics Including Human Applications

558
The inductance in the circuit not only causes the current to lag the emf but it also
reduces the current to a smaller value than it would have if there were no inductance
present. The voltage drop V across an inductance L is given by
V = I?L = 2pƒLI          (25.7)
where ƒ is the frequency in cycles per second and L is the inductance in the circuit in
henries. It follows that the AC current in an inductance is given by the voltage drop
across the inductance divided by 2pƒ times the inductance,
I = V/(2 ƒL)            (25.8)
The factor 2pfL is called the inductive reactance of the circuit, represented by X
L
, and is
measured in ohms L is in henries and f is the frequency (in Hz),
X
L
= 2pƒL            (25.9)
An inductive element in an AC circuit acts as an inertia element and impedes the
alternating current. We also note that this effect depends directly upon the frequency.
Hence for high frequency an inductor exhibits a large inertia and thus greatly impedes a
high-frequency alternating current.
If you connect a capacitor to an AC source the plates of the capacitor become
charged alternatively positive and negative, according to the surge of charges back and
forth in the connecting wires. So, even though there can be no constant DC current
through a capacitor, we can say that there can be an alternating current through a
capacitor. A capacitor does present an impedance to an alternating current which is
called capacitive reactance. We shall represent the capacitive reactance by X
c
. In a way
analogous to the definition of capacitance as the ratio of voltage to charge, we shall
define the capacitive reactance as the ratio of the voltage drop across the capacitor to the
current through the capacitor,
X
c
= V/I            (25.10)
where
X
c
= 1/(2pƒC) ohms           (25.11)
and C is the capacitance in farads and ƒ is the frequency in cycles per second (Hz). Note
that the capacitive reactance decreases as the frequency increases. A capacitor has
infinite impedance for DC sources. The inertia effect of a capacitor in an AC circuit
decreases as the frequency increases.
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