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4.16\u00a0 \u00a0AC circuits<\/p>\n
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- \n
- Understand that the root mean square (RMS) value of a sine wave has the same heating effect as a direct current of the same value and that it is equal to 0.707 of it\u2019s peak value.<\/strong><\/em><\/li>\n<\/ul>\n
[\/et_pb_text][et_pb_toggle title=”Sine Wave Values ” _builder_version=”4.9.10″ _module_preset=”default” title_font=”|700|||||||” title_font_size=”14px” custom_margin=”-35px|||||” custom_padding=”||9px|||”]<\/p>\n
To work with Sine waves there are several definitions which must be understood:<\/p>\n
Amplitude<\/u><\/strong>\u00a0means largeness, width or breadth.\u00a0 In our context it refers to the variation of the wave from zero. It can be measured as either a Peak Value or Peak\u2011to\u2011Peak value.<\/p>\n
The Peak value<\/u><\/strong>\u00a0is the maximum value the wave attains.\u00a0 In the first example above it is 1V.\u00a0 The phase (+ or \u2013 ) does not matter \u2013\u00a0 the Max value is 1 volt<\/p>\n
The Peak to Peak value<\/u><\/strong>\u00a0is the variation between max in one direction and max in the other.\u00a0 In the top example it is 2V.\u00a0 +1V to \u20131V = 2V.<\/p>\n
Average Value<\/u><\/strong>\u00a0is the average of the wave.\u00a0 The average value of a Sine wave is 0\u00d7637 of its peak value.<\/p>\n
RMS Value<\/u><\/strong> The RMS (Root Mean Square) value is 0\u00d7707 of its peak value. The RMS value is the value specified for all house wiring in Australia. Its value is 230 Volts RMS.<\/p>\n
The RMS value of a sine wave is that value that produces an equivalent heating effect in a resistive load as the same voltage from a DC source.<\/p>\n
So a 230 Volt RMS source supplying a resistive load of one hundred ohms will produce a current of<\/p>\n
I = V\/R<\/p>\n
= 230\/100<\/p>\n
=\u00a0 2\u03873 Amps<\/p>\n
The power dissipated in the resistor will be<\/p>\n
P = I2<\/sup>R<\/p>\n
= 2\u03873 * 2\u03873 * 100<\/p>\n
=\u00a0 529 Watts<\/p>\n
If we connected a 230 Volt DC source to our 100 ohm resistor and used the same formulas we would have,<\/p>\n
I = 2.3 Amps<\/p>\n
P=\u00a0 529 Watts.<\/p>\n
When specifying or reading the value of an AC source it is essential that you know what value you are reading. \u00a0Is it the Peak value, the Peak to Peak value, the Average value or the RMS value. This may seem confusing but if you remember the relationships for each value of an AC source you can calculate the value you are interested in if given any one of the other values.<\/p>\n
Example.<\/strong><\/p>\n
We know that our household wiring is 230 Volts RMS. What are the Peak, Peak to Peak and Average values?<\/p>\n
Peak Value<\/strong><\/p>\n
V Peak = 1\u0387414 * RMS<\/p>\n
=\u00a0 1\u0387414 * 230<\/p>\n
=\u00a0\u00a0 325.22 Volts<\/p>\n
Peak to Peak Value<\/strong><\/p>\n
V Peak to Peak = 2 * V Peak<\/p>\n
= 2 * 325.22<\/p>\n
= 650.44 Volts<\/p>\n
Or working from our RMS value<\/p>\n
V Peak to Peak = 2\u0387828 * RMS<\/p>\n
=\u00a0 2\u0387828 * 230<\/p>\n
=\u00a0 650.44 Volts<\/p>\n
Average Value<\/strong><\/p>\n
V Average = 0\u0387637 * V Peak<\/p>\n
=\u00a0 0\u0387637 * 325.22<\/p>\n
=\u00a0\u00a0 207\u038717 Volts<\/p>\n
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4.17<\/p>\n
[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_3″ _builder_version=”4.9.10″ _module_preset=”default”][et_pb_text _builder_version=”4.9.10″ _module_preset=”default” custom_margin=”||-4px|||” custom_padding=”||2px|||”]<\/p>\n
- \n
- Recall that the period (time) of a sine wave is equal to 1\/f seconds and that the frequency of a sine wave is equal to 1\/T (where f = frequency in Hertz and T = time in seconds).<\/strong><\/em><\/li>\n<\/ul>\n
[\/et_pb_text][et_pb_toggle title=”Frequency and Period” _builder_version=”4.9.10″ _module_preset=”default” title_font=”|700|||||||” title_font_size=”14px” custom_padding=”10px|||||”]<\/p>\n
\u00a0One complete revolution of a rotating conductor in a magnetic field produces one cycle.\u00a0 A cycle is the amount of time from a point on a sine wave to a point on the next wave of the same amplitude and polarity.<\/p>\n
The frequency of a sine wave is the number of cycles per second measured in Hertz (Hz). The time it takes to complete one cycle is known as the period of the waveform. Our household power has a frequency of 50 Hz. Fifty complete cycles occur in one second.<\/p>\n
The time taken for just one cycle is the period of the waveform and is calculated from the following formula<\/p>\n
Period (in seconds) \u00a0= 1 \/ Frequency in Hertz<\/p>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>T = 1<\/sup>\/f<\/sub><\/p>\n
Example<\/strong><\/p>\n
What is the period of an AC waveform that has a frequency of 50 Hz<\/p>\n
T = 1 \/50<\/p>\n
=\u00a0 0\u038702 Second<\/p>\n
= 20 mS<\/p>\n
<\/a>Frequency and Wavelength<\/strong><\/p>\n
The wavelength of a sine wave is the distance travelled by the leading point of one cycle. Since a sine wave propagates at the speed of light, 300,000,000 meters per second, if its frequency is known the wavelength can be calculated from the following formula. The symbol for wavelength is l (lambda).<\/p>\n
The relationship with frequency is,<\/p>\n
l (in meters) =\u00a0 300,000,000 \u00b8 f (in Hertz) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0or\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0f (in Hertz) = 300,000,000 \u00b8 l (in meters)<\/p>\n
It is often easier to use:<\/p>\n
l (m) = 300 \u00b8 f (MHz)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 or\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 f (MHz) = 300 \u00b8 l (m)<\/p>\n
[\/et_pb_toggle][\/et_pb_column][\/et_pb_row][et_pb_row column_structure=”1_3,2_3″ _builder_version=”4.9.10″ _module_preset=”default” custom_padding=”||0px|||”][et_pb_column type=”1_3″ _builder_version=”4.9.10″ _module_preset=”default”][et_pb_text _builder_version=”4.9.10″ _module_preset=”default”]<\/p>\n
4.18<\/p>\n
[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_3″ _builder_version=”4.9.10″ _module_preset=”default”][et_pb_text _builder_version=”4.9.10″ _module_preset=”default” min_height=”78.4px” custom_margin=”||-12px|||” custom_padding=”||2px|||”]<\/p>\n
- \n
- Understand that AC waveforms are expressed in degrees and that a complete cycle is equal to 360 degrees.<\/strong><\/em><\/li>\n<\/ul>\n
[\/et_pb_text][et_pb_toggle title=”Sine wave period” _builder_version=”4.9.10″ _module_preset=”default” title_font=”|700|||||||” title_font_size=”14px”]<\/p>\n
![](\"https:\/\/www.asc.ohio-state.edu\/price.566\/courses\/694\/images\/circleUnit.jpg\")
<\/p>\nTo create the sine wave curve pictured\u00a0 below, consider the illustration above. Imagine the hypotenuse, C, of the triangle sweeping around the circle in a counter-clockwise rotation. At each point along the sweep, you get back the length of A on the Y axis. The circle is 1 unit in radius, so the value goes from 0 to 1, then back to 0, then 0 to -1 and back to 0 again.The reason you get the “sine wave” curve below is that you are progressing through the values of the ‘sweep’ over time.<\/span><\/p>\n
The sin() function uses as its input the angle,\u00a0<\/span>
![](\"https:\/\/www.asc.ohio-state.edu\/price.566\/courses\/694\/images\/inline.gif\")
, of the counter-clockwise ‘sweep’, in radians, not degrees.<\/span>
There are 2* PI radians in 360 degrees.<\/span>
radians = degrees * (PI \/ 180)<\/span>
degrees = radians * (180 \/ PI)<\/span><\/p>\n![](\"https:\/\/www.asc.ohio-state.edu\/price.566\/courses\/694\/images\/sin.jpg\")
<\/span><\/span><\/p>\n[\/et_pb_toggle][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”4.9.10″ _module_preset=”default” custom_padding=”0px||0px|||”][et_pb_row column_structure=”1_3,2_3″ _builder_version=”4.9.10″ _module_preset=”default” custom_padding=”||0px|||”][et_pb_column type=”1_3″ _builder_version=”4.9.10″ _module_preset=”default”][et_pb_text _builder_version=”4.9.10″ _module_preset=”default”]<\/p>\n
4.19\u00a0 Phase and impedance<\/p>\n
[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_3″ _builder_version=”4.9.10″ _module_preset=”default”][et_pb_text _builder_version=”4.9.10″ _module_preset=”default” min_height=”34.6px” custom_margin=”||29px|||” custom_padding=”||2px|||”]<\/p>\n
- \n
- Recall that for a resistor, the PD and current are in phase.<\/strong><\/em><\/li>\n
- Recall that current lags potential difference by 90 degrees in an inductor and that current leads by 90 degrees in a capacitor.<\/strong><\/em><\/li>\n
- Recall that the term \u2018reactance\u2019 describes the opposition to current flow in a purely inductive or capacitive circuit \u00a0\u00a0\u00a0\u00a0\u00a0where the phase difference between E and I is 90 degrees.<\/strong><\/em><\/li>\n
- Understand and apply the equations for inductive and capacitive reactance. Understand the application of the formulae XL=2\u03c0FL and XC= 1\/2\u03c0FC<\/strong><\/em><\/li>\n<\/ul>\n
[\/et_pb_text][et_pb_toggle title=”Phase shift” _builder_version=”4.9.10″ _module_preset=”default” title_font=”|700|||||||” title_font_size=”14px” custom_margin=”-35px|||||” custom_padding=”||9px|||”]<\/p>\n
Generally, AC circuits may contain Resistors, Inductors and (or) Capacitors. Impedance, represented by the letter “Z” and measured in Ohms, is the total opposition that a circuit offers to the flow of AC Current, it is a combination of Resistance R and Reactance X, Z = R + jX, Figure 1.<\/p>\n
![\"\"](\"https:\/\/vk6gmd.com.au\/wp-content\/uploads\/2021\/07\/phase1-300x215.png\")
\u00a0<\/p>\nFigure 1: Impedance Diagram<\/p>\n
In AC circuits, because the existence of Reactive Components, the Voltage and Current may not reach the same amplitude peaks at the same time, they generally have a difference in timing. This timing difference is called Phase Shift, f, 0\u00b0 \u2264 f \u2264 90\u00b0, and is measured in angular degrees.<\/p>\n
A circuit that contains only Resistors is called Resistive Circuit. There is no Phase Shift between the Voltage and the Current in a Resistive Circuit, \u03a6 = 0\u00b0, Figure 2a. The Current is “In-Phase” with the Voltage.<\/p>\n
![\"\"](\"https:\/\/vk6gmd.com.au\/wp-content\/uploads\/2021\/07\/phase2-300x102.png\")
<\/p>\nFigure 2a: V-I Relationship of the Circuit R<\/p>\n
Capacitors and Inductors are called Reactive Components, in which the Voltage and Current are “Out-of-Phase” with each other. In an Inductor, the Voltage leads the Current by 90\u00b0, \u03a6 = 90\u00b0, Figure 2b; in a Capacitor, the Voltage lags the Current by 90\u00b0, \u03a6 = -90\u00b0, Figure 2c.<\/p>\n
![\"\"](\"https:\/\/vk6gmd.com.au\/wp-content\/uploads\/2021\/07\/phase3-300x104.png\")
<\/p>\nFigure 2b: V-I Relationship of Circuit L<\/p>\n
![\"\"](\"https:\/\/vk6gmd.com.au\/wp-content\/uploads\/2021\/07\/phase4-300x126.png\")
<\/p>\nFigure 2c: V-I Relationship of Circuit C<\/p>\n
A circuit that contains Inductors and (or) Capacitors is called Reactive Circuit, which can be classified into Inductive Circuit, XL<\/sub>\u00a0<\/span>> XC<\/sub>, and Capacitive Circuit, XC<\/sub>\u00a0<\/span>> XL<\/sub>.<\/p>\n
Figure 3a shows an Inductive Circuit that consists of R and L in series. As the Inductor opposes a change in Current and stores energy from the Power Supply in the form of a Magnetic Field, the Inductor Voltage vL<\/sub>\u00a0<\/span>leads the Inductor Current iL<\/sub>\u00a0<\/span>by 90\u00b0 and leads the Power Supply Voltage v by a Phase Angle \u03a6.<\/p>\n
![\"\"](\"https:\/\/vk6gmd.com.au\/wp-content\/uploads\/2021\/07\/phase5-300x127.png\")
<\/p>\nFigure 3a: V-I Relationship of the Circuit RL<\/p>\n
Figure 3b shows a Capacitive Circuit that consists of R and C in series. As the Capacitor opposes a change in Voltage and stores energy from the Power Supply in the form of an Electric Field, the Capacitor Voltage vC<\/sub>\u00a0<\/span>lags the Capacitor Current iC<\/sub>\u00a0<\/span>by 90\u00b0 and lags the Power Supply Voltage v by a Phase Angle \u03a6.<\/p>\n
![\"\"](\"https:\/\/vk6gmd.com.au\/wp-content\/uploads\/2021\/07\/phase6-300x160.png\")
<\/p>\nFigure 3b: V-I Relationship of the Circuits RC<\/p>\n
[\/et_pb_toggle][et_pb_toggle title=”Reactance” _builder_version=”4.9.10″ _module_preset=”default” title_font=”|700|||||||” title_font_size=”14px” custom_margin=”-14px|||||” custom_padding=”||9px|||”]<\/p>\n
Capacitive Reactance<\/strong><\/p>\n
In an AC circuit a capacitor is continually charging and discharging and its opposition to the change is called capacitive reactance (XC<\/sub>). It is similar to resistance and is measured in Ohms.<\/p>\n
\u00a0Unlike resistance no power is dissipated by reactance.\u00a0 The energy is \u2018borrowed\u2019 during one part of the cycle and \u2018paid back\u2019 during the next part. Because capacitors do not charge instantly the amount of charge and therefore its opposition or reactance is affected by frequency.<\/p>\n
The formula for calculating the reactance of a capacitor is:<\/p>\n
XC<\/sub> =\u00a0 1<\/sup>\/2\u03c0fC <\/sub>\u00a0<\/p>\n
Where XC<\/sub> is the reactance in W (Ohms);\u00a0<\/p>\n
f is the frequency in Hz (Hertz); &<\/p>\n
C in capacitance in F (Farads).<\/p>\n
As XC<\/sub> is inversely related to frequency the reactance will decrease when frequency increases.<\/p>\n
Imagine a light globe connected in series with a capacitor and an EMF.\u00a0 If the EMF is DC the globe will light very briefly as the capacitor charges, dimming down as the current flow reduces and will go out when the cap is charged as there is no current flow.\u00a0<\/p>\n
If the EMF is AC with a low frequency the globe will light and dim as the capacitor charges\/discharges and the current flow changes.\u00a0 As the frequency is increased the globe will get brighter as the capacitor does not fully charge\/discharge and the current flow is greater.\u00a0<\/strong><\/p>\n
Example 1:<\/strong><\/p>\n
What is the reactance of a 20nF capacitor operating in a circuit with a frequency of 6kHz.<\/p>\n
XC<\/sub> = 1<\/sup>\/2<\/sub>\u03a0<\/sub>fC<\/sub><\/p>\n
\u00a0\u00a0\u00a0\u00a0\u00a0 = 1 \/ 6\u2219283*6E3*20E-9<\/p>\n
\u00a0\u00a0\u00a0\u00a0\u00a0 = 1 \/ 753\u221996E-6<\/p>\n
\u00a0\u00a0\u00a0\u00a0 \u00a0= 1326\u221933\u2126<\/p>\n
Example 2:<\/strong><\/p>\n
If we double the operating frequency.\u00a0 A 20nF capacitor operating at 12kHz<\/p>\n
XC<\/sub>\u00a0 =\u00a0 1<\/sup> \/ 6\u2219283*12E3*20E-9<\/sub><\/p>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0 1<\/sup> \/ 1507\u221992E-6<\/sub><\/p>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = \u00a0663\u221916\u2126<\/sub><\/p>\n
Inductive Reactance<\/strong><\/p>\n
According to Faraday\u2019s law of Induced Voltage the voltage depends on the strength of the magnetic flux, the number of turns in the coil and the speed of the relative movement.<\/p>\n
In an AC circuit the magnetic field surrounding the inductor is continually building and collapsing in time with the current flow.\u00a0 The field from each turn of the coil will cut the adjacent turns inducing an opposing current. \u00a0This is known as a \u2018back EMF\u2019.<\/p>\n
Because the value of the induced voltage depends on the speed of the relative movement between the magnetic field and the conductor, the value of\u00a0 the back EMF will depend on the AC frequency.\u00a0 The higher the frequency the more direction changes per second and therefore the faster the rate of change or speed of relative movement.<\/p>\n
Inductive reactance increases with frequency\u00a0<\/p>\n
The opposition is called inductive reactance (XL<\/sub>). It is similar to resistance and is measured in Ohms.<\/p>\n
Remember, unlike resistance no power is dissipated by reactance.\u00a0<\/p>\n
The formula for calculating reactance of an inductor is:<\/p>\n
XL<\/sub> =\u00a0 2\u03c0fL <\/sub>\u00a0<\/p>\n
Where Xl<\/sub> is the reactance in W (Ohms);\u00a0<\/p>\n
f is the frequency in Hz (Hertz); &<\/p>\n
L is the inductance in H (Henry\u2019s).<\/p>\n
Example:\u00a0 <\/strong>\u00a0\u00a0<\/p>\n
If an inductance of 50mH is supplied by an AC source with a frequency of 50Hz, what is its XL<\/sub>.\u00a0<\/p>\n
XL<\/sub> = 2\u03c0fL<\/p>\n
\u00a0\u00a0\u00a0 \u00a0= 2*3\u2219141*50*50E-3<\/p>\n
\u00a0\u00a0\u00a0\u00a0 = 15.7\u2126\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n
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4.20<\/p>\n
[\/et_pb_text][\/et_pb_column][et_pb_column type=”2_3″ _builder_version=”4.9.10″ _module_preset=”default”][et_pb_text _builder_version=”4.9.10″ _module_preset=”default” custom_margin=”||-4px|||” custom_padding=”||2px|||”]<\/p>\n
- \n
- Understand that impedance is a combination of resistance and reactance and apply the formulae for impedance and current in a series CR or LR circuit.<\/strong><\/em><\/li>\n<\/ul>\n
[\/et_pb_text][et_pb_toggle title=”Impedance” _builder_version=”4.9.10″ _module_preset=”default” title_font=”|700|||||||” title_font_size=”14px” custom_padding=”10px|||||”]<\/p>\n
Impedance and reactance<\/h2>\n
An element in a DC circuit can be described using only its\u00a0<\/span>resistance<\/a>. The resistance of a capacitor in a DC circuit is regarded as an open connection (infinite resistance), while the resistance of an inductor in a DC circuit is regarded as a short connection (zero resistance). In other words, using capacitors or inductors in an ideal DC circuit would be a waste of components. Yet, they are still used in real circuits and the reason is that they never operate with ideally constant voltages and currents.<\/p>\n
As opposed to constant voltage circuits, in AC circuits the impedance of an element is a measure of how much the element opposes current flow when an AC voltage is applied across it. It is basically a voltage to current ratio, expressed in the frequency domain. Impedance is a complex number, which consists of a real and an imaginary part:<\/p>\n
![\"impedance-reactance\"](\"https:\/\/eepower.com\/uploads\/education\/impedance-reactance.png\")
<\/p>\nwhere\u00a0<\/span>Z<\/em>\u00a0<\/span>is the complex impedance. The real part\u00a0<\/span>R<\/em>\u00a0<\/span>represents resistance, while the imaginary part\u00a0<\/span>X<\/em>\u00a0<\/span>represents reactance. Resistance is always positive, while reactance can be either positive or negative. Resistance in a circuit dissipates power as heat, while reactance stores energy in the form of an electric or magnetic field.<\/p>\n
Impedance of a resistor<\/h3>\n
- Recall that current lags potential difference by 90 degrees in an inductor and that current leads by 90 degrees in a capacitor.<\/strong><\/em><\/li>\n
- Recall that for a resistor, the PD and current are in phase.<\/strong><\/em><\/li>\n
- Understand that AC waveforms are expressed in degrees and that a complete cycle is equal to 360 degrees.<\/strong><\/em><\/li>\n<\/ul>\n
- Recall that the period (time) of a sine wave is equal to 1\/f seconds and that the frequency of a sine wave is equal to 1\/T (where f = frequency in Hertz and T = time in seconds).<\/strong><\/em><\/li>\n<\/ul>\n
![\"impedance-resistor\"](\"https:\/\/eepower.com\/uploads\/education\/impedance-resistor.png\")
<\/p>\n![\"resistor](\"https:\/\/eepower.com\/uploads\/education\/resistor-cv.png\")
<\/h2>\n![\"capacitor](\"https:\/\/eepower.com\/uploads\/education\/capacitor-cv.png\")
<\/p>\n![\"impedance-capacitor\"](\"https:\/\/eepower.com\/uploads\/education\/impedance-capacitor.png\")
<\/p>\n![\"inductor](\"https:\/\/eepower.com\/uploads\/education\/inductor-cv.png\")
<\/p>\n![\"impedance-inductor\"](\"https:\/\/eepower.com\/uploads\/education\/impedance-inductor.png\")
<\/p>\n![\"ohms-law\"](\"https:\/\/eepower.com\/uploads\/education\/ohms-law.png\")
<\/p>\n![\"ohms-law-complex\"](\"https:\/\/eepower.com\/uploads\/education\/ohms-law-complex.png\")
<\/p>\n![\"Voltage](\"https:\/\/eepower.com\/uploads\/education\/voltage-ac-circuit.png\")
<\/p>\n![\"Voltage](\"https:\/\/eepower.com\/uploads\/education\/voltage-ac-circuit-complex.png\")
<\/p>\n![\"equivalent1\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent1.png\")
<\/p>\n![\"equivalent2\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent2.png\")
<\/p>\n![\"equivalent3\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent3.png\")
<\/p>\n![\"equivalent4\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent4.png\")
<\/p>\n![\"equivalent5\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent5.png\")
<\/p>\n![\"equivalent6\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent6.png\")
<\/p>\n![\"equivalent7\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent7.png\")
<\/p>\n![\"equivalent8\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent8.png\")
<\/p>\n![\"equivalent9\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent9.png\")
<\/p>\n![\"equivalent10\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent10.png\")
<\/p>\n![\"equivalent11\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent11.png\")
<\/p>\n![\"equivalent12\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent12.png\")
<\/p>\n![\"equivalent13\"](\"https:\/\/eepower.com\/uploads\/education\/equivalent13.png\")
<\/p>\n