Materi Arus dan Tegangan Listrik Bolak-balik (english version)

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Alternating Current (AC)



Previously we have learned about direct current electricity, i.e. the electric current and voltage whose magnitude can be considered fixed and flowing in one direction. Direct current, also called direct current (DC), for example, is produced by a battery (see picture above).

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In this teaching material will be discussed about alternating current or alternating current (AC), i.e. the electric current and voltage whose magnitude changes with time and can flow in two directions. Alternating current is widely used for lighting and electronic equipment such as televisions, radios, microwave ovens, and others. In Indonesia, alternating current electricity is provided by PLN. In this teaching material, you will also learn several electrical components, including resistors, inductors, and capacitors, as well as circuits that use these electrical components

GENERATOR

electric-generators

A generator is a machine that converts kinetic (mechanical) energy into electrical energy (see picture above). The working principle of the generator is to produce an electric current induced by rotating the coil in a magnetic field

ac_generatorBased on the type of induced emf or induced electric current generated, generators can be distinguished from alternating current generators (AC) and direct current generators (DC). The difference between direct current generators and alternating current generators is only in the glide ring (collector ring) which is related to both ends of the coil where the AC generator has two rings, each of which is connected to each end of the coil while the DC generator has a ring that is split in the middle which is called a split ring or commutator.

A simple AC generator consists of a coil that is rotated in a magnetic field like the picture shown above. To see how the current is generated by the generator, consider the two vertical sides of the coil in the picture.

For the coil to rotate counter-clockwise then the left vertical side must experience a forward F force and the right vertical side must experience a backward F force. In accordance with the rules of the palm for the magnetic force (Lorentz force), the current I on the left vertical side must be upward, and the current I on the right vertical side must be downward, as shown in the figure. The direction of the force F in the image is in the direction of the normal direction of the coil plane n, thus the angle between the magnetic induction direction B and the normal direction field n is θ. In a generator, the rotation of the coil causes the angle θ to always change, and this causes the magnetic flux (Ф), which breaks through the plane of the coil to also change. At the ends of the loop wire an induced emf (ε) is generated, which can be calculated by the equation:

ε=-NBA (d cosθ)/dt

If the loop is rotated with angular velocity ω then θ = ωt, and the above equation can be written as:

ε=-NBA (d )/dt(cos⁡(ωt)
ε=NBA ω sin⁡ωt

If the maximum induced emf between the brush tips is equal to ε_m, then the above equation can be written as:

ε=ε_m sin⁡〖ωt=〗 NBA ω sin⁡ωt

With a maximum emf, ε_m, given by:

ε_m=NBAω

With ε = instantaneous induced emf
ε_m = maximum induced emf
ω = rotational angle velocity of the loop
t = loop length has been rotating. It is evident that the induced emf generated in the loop changes with time every one period T = 2π / ω.

CURRENT FLOWS AND VOLTAGE

Alternating current and voltage are currents and voltages whose values ​​change with time periodically. Such magnitude is called alternating current and AC (Alternating Current). If in direct current you can find out the value and the voltage is always fixed. Then, in alternating current you will be able to find out the maximum value generated and the oscillation frequency generated by the source. Alternating electric current and voltage in the form of sinusoid as shown in Figure below.


Mathematically, the alternating current and voltage can be stated as follows:
V=V_{m}sinomega .t=V_{m}sin2pi .f.t=t=V_{m}sin2pi frac{t}{T} I=I_{m}sinomega .t=I_{m}sin2pi .f.t=t=I_{m}sin2pi frac{t}{T}

Where:

V = instantaneous voltage (V)

I = instantaneous current (A)

Vm = maximum voltage (V)

Im = maximum current (A)

f = frequency (Hz)

T = period (s)

t = time (s)

ωt = phase angle (radians or degrees)

The relationship of the amplitude of alternating voltage or current to the phase angle can be expressed graphically in the phasor diagram. A phasor is a vector that rotates counterclockwise with respect to the origin at angular velocity ω.

The phasor of a quantity is described as a vector whose rotation angle with respect to the horizontal axis (x axis) is the same as the phase angle. The maximum value of the magnitude is the same as the length of the phasor, while the momentary value is the phasor projection on the vertical axis (y axis). Here is a picture of a phasor diagram for current and voltage with the same phase angle (phase) and a picture of the time function of the current and voltage.


In fact, alternating current and voltage are not vector quantities, but scalar quantities. The depiction of alternating current and voltage as phasors is to facilitate the analysis of more complicated alternating current circuits



AVERAGE VALUE AND EFFECTIVE VALUE

The average value of alternating current is the strength of alternating current whose value is equivalent to the strength of direct current to move the same amount of electric charge at the same time. Average flow is expressed by:
I_{r}=frac{2I_{m}}{pi }

While the average stress is expressed by:
V_{r}=frac{2V_{m}}{pi }

The effective value of alternating current and voltage is alternating current and voltage equal to direct current and voltage to produce the same amount of heat when passing through a resistor at the same time. 

Mathematically, the relationship between effective current and voltage with maximum current and voltage is expressed by: 
I_{ef}=frac{I_{m}}{sqrt{2} } V_{ef}=frac{V_{m}}{sqrt{2} }

Problems example

1. The electrical grid at home has 220 volts. An electrical device with a resistance of 50 ohms is installed on the net. Count it: a. Effective and maximum value of voltage b. Effective and maximum value of electric current flowing

Settlement:

a. Voltage measurement results are effective values, so: Vef = 220 volt dan R = 50 Ω Vef = 220 volt Vmax = V_ef √2=220√2 volt

b. Use Ohm's law to determine the strong current. I_ef=V_ef/R=220/50=4,4 A I_m=V_m/R=(220√2)/50=22/5 √2 A

2. An AC generator produces voltage as a function of time as follows: V = 200√2 sin⁡ ⁡ 50t volt. Calculate:

a. Maximum voltage b. Peak to peak voltage c. Effective voltage d. Angular frequency e. Period f. Frequency g. Voltage at 0.01 seconds

Settlement: 

Compare the general equation of voltage with a known equation:

V=V_m sin⁡ωt volt V=200√2 sin⁡〖50t volt〗 a. V_m=200√2 volt b. Peak to peak voltage is equal to twice the maximum voltage

c. Vpp = 2Vm = 2 . 200√2 volt = 400√2 volt d. V_ef=V_m/√2=(200√2)/√2=200 volt e. ω=50 rad/s ω=2π/T → T=2π/ω=2π/50=π/25 s f. f=1/T=1/(π⁄25)=25/π Hz g. V pada t = 0,01 π sekon: V=200√2 sin⁡50t=200√2 sin⁡〖50 (0,01π)〗 V=200√2 sin⁡〖0,5π=200√2 sin⁡〖〖90〗^o=〗 〗 200√2 volt

Measuring Voltage and Alternating Current


Alternating voltage and electric current are measured with an AC voltmeter and an AC ammeter (see the picture above). By using a voltmeter or AC ammeter the measured value is the value of rms (root mean squere) = average square root current =; = the average of or the effective value of voltage or current. In general, the results of measurements of voltage (V) and current (I) can be written as follows:

I = (Needle designation) / (Maximum scale) × Maximum measurement limit

V = (Needle designation) / (Maximum scale) × Maximum measurement limit

Problems example
An AC ammeter is used to measure the alternating current strength so that the ammeter needle shows the number as shown in the picture on the right. Determine: 

a. Effective value 
b. Maximum Value 
c. Average value of alternating current

Settlement:

The electrical circuit wire is connected to the current terminal 0 A and 10 A, meaning that the maximum measurement limit of amperemeter is 10 A. Ammeters scale is 0 to 50, so if the amperemeter needle shows the number 50 then the measurement result is maximum, 10 A. Ammeters designation is an effective value so that: a. I_ef=40/50×10=8 A b. Nilai maksimum I_m=I_ef √2=8√2 A c. Nilai rata-rata I_r=(2I_m)/π=(2×8√2)/π=16/π √2 A

To see the form of sinusoidal voltage or current generated by an alternating source, an oscilloscope can be used (See picture above).

The vertical axis shows the value of the voltage or current generated by an alternating source and the horizontal axis shows the time. From the oscilloscope monitor can be determined the maximum value of the voltage or electric current and from the horizontal axis can be determined the period or frequency of alternating sources. The monitor of an oscilloscope is divided into rows and columns so that they form a box.

Look at the following picture! 

If the vertical axis is set at a voltage of 2 V/cm, the time in the horizontal direction shows 10 ms/cm and each box has a size of 1 cm × 1 cm. Determine: 
a. maximum voltage of AC source; 
b. AC frequency source. 
Settlement: 
a. From the picture can be seen the voltage from peak to peak 

So, the maximum voltage is 4 volts. 
b. The periods of sinusoidal waves that are produced are: 

Vibration Frequency 

So the frequency of the AC source is 25 Hz.

Alternating Current Circuit

Basically, the components of the electrical circuit show different characteristics when connected to a direct voltage source and when connected to an alternating voltage source.

Therefore, the characteristics of a direct current circuit differ from the characteristics of an alternating current circuit and one of the differences is related to the phase between voltage and current.

In general, all electrical circuits have resistance, capacity, and inductance even though there are no resistors, capacitors, and inductors.

However, the value of the obstacles, capacity, and inductance depends on the type of component contained in the circuit, and maybe in certain circumstances the value of the obstacles, capacity, and inductance can be ignored, whereas in other circumstances it may not be ignored

Theoretically it can be assumed that the electrical circuit consists of a resistive circuit, an inductive circuit, and a capacitive circuit

RANGKAIAN RESISTIF

Resistive circuit is a circuit that only consists of a voltage source (V) with a resistor that has resistance R and the value of capacity (C) and inductance (L) the circuit is ignored. Consider an alternating current circuit consisting of a resistor and an AC generator as shown below:


he voltage on the VR resistor is the same as the generator voltage so that the resistive circuit can be written:

V_R=V_m sin⁡ωt

I_R=V_m/R sin⁡ωt= I_m sin⁡ωt

Thus the following relationship will also apply:

I_m=V_m/R

I_ef=V_ef/R

Because resistive circuits are considered to have no inductance and capacity, resistive circuits are not affected by changes in the surrounding magnetic field. Based on this, then in the resistive circuit, alternating current and voltage have the same phase or zero phase difference.

RANGKAIAN INDUKTIF

Inductive circuit is a circuit that only consists of a voltage source (V) with inductors that have inductance L and the values ​​of resistance (R) and capacity (C) of the circuit are ignored, as shown in the following figure:

The current flowing in the pure inductive circuit changes with time that satisfies the equation I = I_m sin⁡ 〖ω t,〗 so that the inductor is induced by an electromotive force which satisfies the equation:

ε_ind=-L dI/dt=-L d(I_m sin⁡ωt )/dt

Although there is no resistor in the inductive circuit, but in this circuit there is a quantity that has the same properties as the electrical resistance, namely inductive reactance, the magnitude of which can be determined as follows:

X_L=ωL=2πfL

With: X_L = inductive reactance (Ω) ω = angular velocity (rad / s) f = AC source frequency (Hz) L = inductor inductor (H)

RANGKAIAN KAPASITIF

Capacitive circuit is a circuit that only consists of a voltage source (V) with a capacitor that has a capacity of C and the values ​​of resistance (R) and inductance (L) the circuit is ignored, as shown in the following figure:


As in the inductive circuit, in the capacitive circuit there is a quantity of reactance called capacitive reactance and the amount can be determined as follows:

X_C=1/ωC=1/2πfC

With: X_C = capacitive reactance (Ω) C = capacitor capacity (F)

Problems example

1. A pure inductive alternating current circuit consists of an inductor with an inductance L = 25 mH and an AC voltage source with an effective voltage of 150 V. The inductive reactance Effective current strength of the circuit if the source frequency is 50 Hz.

Settlement: X_L=ωL=2πfL=2π(50)(25×〖10〗^(-3) )=7,85 Ω I_ef=V_ef/X_L =150/7,85=19,1 A

2. An 8 μF capacitor is connected to an AC voltage source whose effective voltage is 150 V and its frequency is f = 50 Hz. How much: Capacitive reactance Effective current in a circuit

Settlement:
X_C=1/ωC=1/2πfC=1/(2π(50)(8×〖10〗^(-6)))=397,89 Ω
I_ef=V_ef/X_C =150/397,89=0,38 A

SERIES OF R-L-C SERIES

In the previous learning activity, it was discussed how the influence of resistors, inductors, and capacitors connected separately with an alternating current source I = I_m sin⁡ωt. Now it will be reviewed, what will happen if the three elements are connected in series, which is often called the RLC series circuit as shown above.

THE RELATIONSHIP OF VR, VL, VC, AND V ON RLC SERIES


To determine the relationship between VR, VL, and VC, a phasor diagram is used. Note that because the three elements are connected in series, the current flowing through all elements is equal, I = I_m sin⁡ωt. In other words alternating current at all points in the RLC series circuit has the same maximum value and phase. However, the stresses on each element will have different values ​​and phases. The voltage at the VR resistor is in phase with current I, the voltage at the VL inductor precedes the current π / 2 rad or 90o, and the voltage on the capacitor lags behind the current π / 2 rad or 90o. Thus it can be written: 

V_R=I_m R sin⁡ωt= V_mR sin⁡ωt V_L=I_m X_L 〖sin 〗⁡〖(ωt〗+〖90〗^o)= V_mL sin⁡〖 (ωt〗+〖90〗^o) V_C=I_m X_C sin⁡〖 (ωt〗-〖90〗^o)= V_mC sin⁡〖 (ωt〗-〖90〗^o)

If the angle ωt is set on the x-axis, the phasor diagram for current I, voltage VR, VL, and VC will look like the following picture.


In accordance with Kirchoff's law, the voltage between the ends of the RLC series circuit, that is VAB = V is the number of phasors between VR, VL, and VC. the addition of the phasor results in the total voltage, which is:

V=√(V_R^2+(V_L-V_C )^2 )

IMPEDANCE OF R-L-C SERIES CIRCUITS

In the DC circuit generally only one type of resistance will be found, namely the pure resistor R, the total resistance value of several resistors connected in series is the algebraic sum (scalar) of each resistance. In the AC circuit, there are resistors, inductors, and capacitors in the circuit. The total resistance effect produced by R, XL, and XC in the AC circuit is called impedance (Z). Z value cannot be calculated by algebraic (scalar) addition as in direct current. To determine the Z value the following equation is used: V=√(V_R^2+(V_L-V_C )^2 ) IZ=√((IR)_^2+(〖IX〗_L-〖IX〗_C )^2 ) IZ=I√((R)_^2+(X_L-X_C )^2 ) Z=√((R)_^2+(X_L-X_C )^2 )

The phase angle difference between the strong current I and the voltage V is:

tan⁡〖θ=(V_L-V_C)/V_R 〗=(〖IX〗_L-〖IX〗_C)/IR

tan⁡〖θ=(X_L-X_C)/R〗
By using the two equations above, a phasor diagram for impedance can be made as shown in the following figure.


Problems example 

The series R-L-C series with R = 80 ohms, XL = 100 ohms, and Xc = 40 ohms. This circuit is connected with alternating voltage with an effective voltage of 220 V. 
Determine: 

a. circuit impedance
b. effective current flowing in the circuit
c. effective voltage between the ends of the inductor

Settlement: 

a. Circuit impedance


b. Effective current in the entire circuit
 
c.Effective voltage between the ends of the inductor
 

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