Ac And Dc Circuits Pdf
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- Understanding DC Circuits By Dale R Patrick and Stephen W Fardo
- Chapter AC – Alternating Current Circuits
- DC Circuits
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At first glance, this graph just shows a jumble of sine waves. They all have the same frequency, but their amplitudes and phases are different.
One of our goals in this chapter is to make some sense of this jumble. The graph actually shows the voltage from an alternating current source like a wall socket , as well as the voltage across a resistor, a capacitor, and an inductor a coil , all of which are connected in a series circuit to the source.
By the end of this chapter, you should be able to determine which graph is which, and to explain their phase relationships and the relationships between the amplitudes. AC stands for alternating current -in fact, both the current and the voltage oscillate sinusoidally. What this means for the light bulb filament is that the current reverses direction at regular intervals.
In North America, in fact, where the frequency of the alternating voltage is 60 Hz, the current changes direction times every second! In addition, at instants during each second, the current is zero, and if you average over each cycle the average current is zero.
The light bulb filament shines brightly despite this, because of all the energy transferred to it from the net motion of the electrons during the periods of non-zero current. In this chapter, we will investigate some of the issues that come up when resistors, capacitors, and inductors coils are connected in AC circuits.
To understand these circuits, we can apply many of the ideas that we applied when we learned about DC circuits. Ohm's law, for instance, applies, as does the loop rule. We will learn some new ideas, too. As usual, the key will be to see how all the new concepts fit into the framework we built when we looked at DC circuits.
We should also keep in mind that AC circuits are all around us -anything that plugs into a wall socket is part of an AC circuit, and many practical devices, such as metal detectors and circuits in stereo systems, exploit various properties of AC circuits. AC-1 Inductors and InductanceIn Essential Physics Chapter 20, Generating Electricity, we discussed Faraday's law and Lenz's law, and explored the tendency of a coil of wire to oppose changes in the magnetic flux passing through the coil.
When we use a coil of wire as part of a circuit as a circuit element, that is , we call the coil an inductor. With an inductor in a circuit, the magnetic field in the coil comes from the current that passes through the coil. If the current is constant, the magnetic flux is constant, and there is no change in flux to oppose. If the current changes, however, there is a corresponding change in magnetic flux, and the coil then acts to oppose the change in flux.
Through Faraday's law, there is an induced voltage across the coil -the coil actually acts like a battery while the flux is changing. If the current through the coil is decreasing, the induced voltage causes an induced current that opposes the change, adding some current back to try to counteract the loss of current.
If the current through the coil is increasing, the induced voltage again causes an induced current that opposes the change, adding some current in the opposite direction to cancel out a fraction of the increased current. All of this is shown below in Figure , showing a constant current, the inductor acts as a resistor, because the length of wire from which the inductor is made has a resistance.
In b , the current in the circuit is directed to the right, and is increasing. This causes an increase in magnetic flux through the coils of the inductor the magnetic field being proportional to the current through the inductor , and the inductor responds by acting as a battery, connected so as to cancel out some of the increase in current. It also acts as a resistor, too, as before. In c , the current in the circuit is directed to the right, and is decreasing. This causes a decrease in magnetic flux through the coils of the inductor, and the inductor responds by acting as a battery, connected so as to cancel out some of the decrease in current.
As before, it also acts as a resistor. The inductance is a measure of how much opposition an inductor provides to a change in the current in the coil. Similar to a capacitor, the inductance of an inductor depends on the geometry such as the number of turns, and the length , as well as on whether there is a magnetic material, such as a piece of iron, inside the coil.
The SI unit of inductance is the henry H. Figure AC. At a particular instant in time, the current in the circuit is 2. At this instant, the potential difference across the capacitor is 5.
At the instant in time described above, what is the potential difference across the resistor, and which end of the resistor is at a higher potential?
The fact that the current is changing is not relevant here. All we need to know is the value of the current in the circuit at the instant we're interested in, and we know that to be 2. The potential difference across the resistor is then given by Ohm's law: 2. Current passes through a resistor from the high potential side to the low potential side, so the left end of the resistor has the higher potential.
Step -The inductor in the circuit has an inductance of 5. At the instant in time described above, what is the potential difference across the inductor, and which end of the inductor is at a higher potential? Assume that the resistance of the inductor is negligible. The magnitude of the potential difference across the inductor is given by: 5.
The current is directed to the right, but decreasing, so the induced voltage across the inductor acts to increase the current. This situation is exactly like that shown in part c of Figure AC. Thus, the right end of the inductor has a higher potential. Answer to Essential Question AC. With the current increasing instead of decreasing, however, the potential difference across the inductor would have the same magnitude as before, but the left end of the inductor would have a higher potential.
In that case, the inductor and resistor would combine to 5. The net potential difference would be zero. In section AC-4, we will address what happens when an alternating current is applied to an RL circuit. For now, however, consider a series RL circuit consisting of a resistor, an inductor, a battery, and a switch.
Such a circuit is similar in form to the RC circuit we investigated in Chapter As we will see, the behavior of the current and voltage in this RL circuit is in many ways opposite to the behavior of current and voltage in the RC circuit, in the sense that the current in the RL circuit behaves like the voltage in the RC circuit, and vice versa.
Initially, there is no current in the circuit. Step 1 -What are the general equations for the potential difference across a resistor, and the potential difference across an inductor? Step 2 -Use the loop rule to find the potential difference across the resistor, and across the inductor, immediately after the switch is moved to the "battery" position.
The inductor opposes changes in current, however, so immediately after the switch is closed, the current is still zero. This means the potential difference across the resistor is zero, and the potential difference across the inductor equals the emf of the battery.
Step 3 -What happens to the potential difference across the inductor, the potential difference across the resistor, and the current in the circuit as time goes by? The current in the circuit, and the potential difference across the resistor, which is proportional to the current, both increase as time goes by. By the loop rule, the potential difference across the inductor decreases as time goes by.
The potential difference across the inductor is proportional to the slope of the current graphthus, the slope of the current graph gradually decreases in magnitude as time goes by. This gives rise to the exponential relationships reflected in Figure AC Step 4 -If we wanted the resistor voltage to increase more quickly, could we change the resistance? If so, how? Could we accomplish this by changing the inductance?
To change the resistor voltage more quickly, we could change the resistance or the inductance. Increasing the resistance decreases the maximum current, so the inductor has a smaller change in current to oppose.
Decreasing the inductance, on the other hand, means that the inductor is less effective at opposing change, so changes occur more quickly. Decreasing the time constant means that quantities change more quickly. Step -When the switch has been in the "battery" position for a long time, the circuit approaches a steady state, in which the current and the resistor voltage both approach their maximum values, and the inductor voltage approaches zero.
If the switch is now moved to the "no battery" position, what happens to the potential difference across the inductor, the potential difference across the resistor, and the current in the circuit as time goes by?
If the inductor was not present, switching the battery out of the circuit would instantly bring the current to zero. With the inductor, the inductor prevents this instantaneous change in current. Instead, the current decreases exponentially to zero, as does the voltage across the resistor. The inductor voltage is the negative of the resistor voltage, by the loop rule, so it also decreases in magnitude as time goes by. This gives rise to the relationships shown in Figure AC-3 AC Circuits with One Circuit Element, part IIn this section, we will investigate a circuit in which a single circuit element either a resistor, a capacitor, or an inductor is connected to a source of alternating voltage, such as a wall socket.
Many people have heard that the voltage from a wall socket is V or V, which clearly differs from the V stated here. This is because to V is an effective average voltage known as the rms rootmean-square voltage.
AC circuit with just a capacitorIn analyzing any AC circuit, the loop rule must be obeyed at all times. We investigated the loop rule in Chapter 18 -it tells us that the sum of the potential differences around a closed loop in a circuit is always zero. When we have just one circuit element connected to an AC source, the implication of the loop rule is that the potential difference across that circuit element must equal the source voltage. The source voltage oscillates sinusoidally, so the potential difference across the single circuit element must oscillate sinusoidally, as well.
For a particular capacitor, the capacitance is constant. Thus, when the voltage oscillates like a sine wave, the charge on the capacitor also follows a sine wave. If we look at the time rate of change of the capacitor voltage the slope of the capacitor voltage vs. With a capacitor, the current is proportional to the slope of the voltage vs.
Understanding DC Circuits By Dale R Patrick and Stephen W Fardo
Most of the examples dealt with so far, and particularly those utilizing batteries, have constant voltage sources. Once the current is established, it is thus also a constant. Direct current DC is the flow of electric charge in only one direction. It is the steady state of a constant-voltage circuit. Most well-known applications, however, use a time-varying voltage source. Alternating current AC is the flow of electric charge that periodically reverses direction.
The book covers Alternating Current AC circuits as well as a brief introduction of electronics. Author: Steven W. Ellingson License: Attribution-ShareAlike. This book is intended to serve as a primary textbook for a one-semester introductory course in undergraduate engineering electromagnetics. Author: James M.
PDF | Deals with D.C. Circuits, Laws Governing D.C. Circuits and Circuit Elements. The value of the voltage or current of an A.C. supply at any instant is called.
Chapter AC – Alternating Current Circuits
Since most circuits and basically all body electrical circuits work on. In ac circuits, the SCR can be turned on by the gate at any angle a with respect to the applied voltage. Find the equivalent resistance between terminals A and D, which then can be used to calculate the source current for a given supply voltage. Established in , it has a membership of around 50, members worldwide.
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DC is the kind of electricity made by a battery with definite positive and negative terminals , or the kind of charge generated by rubbing certain types of materials against each other. Certain sources of electricity most notably, rotary electromechanical generators naturally produce voltages alternating in polarity, reversing positive and negative over time. Whereas the familiar battery symbol is used as a generic symbol for any DC voltage source, the circle with the wavy line inside is the generic symbol for any AC voltage source. One might wonder why anyone would bother with such a thing as AC.
Course Assessment Standards. This is an introductory course, and as such, it assumes that you know very little about electricity. No previous course work in electricity or electronics is required. Basic electrical concepts such as voltage, current, power, and resistance are introduced and examined for DC direct current and AC alternating current. Fundamental laws and relationships such as Ohm's law and power law are developed. Analysis techniques include series-parallel simplification; Thevenin's, Norton's, and superposition theorems; and mesh and nodal analysis. A good scientific calculator with simultaneous equation solution capability will be of great use and is strongly recommended.
Publisher: University of Oklahoma Libraries. This text book covers the basics of DC circuit analysis. It could be considered as a valuable reference book. However, I would not consider it as a text book as it lacks problems. The links provided in the book would make this book a true Comprehensiveness rating: 3 see less. The links provided in the book would make this book a true electronic book.
The major difference between the AC and DC voltage is that in AC voltage the polarity of the wave changes with the time whereas the polarity of the DC voltage always remains same. The other differences between the AC and DC voltage are shown below in the comparison chart. The voltage which causes the alternating current is known as the AC voltage. The alternating current induces in the coil when the current carrying conductor rotates in the magnetic field. The conductor when rotates cuts the magnetic flux and the variation of the flux induces the alternating voltage in the conductor.
a circuit containing a battery is a DC circuit. • in a DC circuit the In an AC circuit the current reverses direction periodically. • AC is what you get from the power.
Number Systems and Codes. Simplification of Switching Functions. Modular Combinational Logic. Introduction to Sequential Devices.
Over the course of the next few chapters, you will learn that AC circuit measurements and calculations can get very complicated due to the complex nature of alternating current in circuits with inductance and capacitance. AC circuit calculations for resistive circuits are the same as for DC. With purely resistive circuits, however, these complexities of AC are of no practical consequence, and so we can treat the numbers as though we were dealing with simple DC quantities. One major caveat needs to be given here: all measurements of AC voltage and current must be expressed in the same terms peak, peak-to-peak, average, or RMS. If the source voltage is given in peak AC volts, then all currents and voltages subsequently calculated are cast in terms of peak units.
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