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The real part of the impedance $Z_{aa'}$ is resistive so all you need to decide as to what component, inductor or capacitor, you would assign a negative imaginary part to. Perhaps do it by a process of elimination or write down the general formulae for the reactances of capacitors and inductors?


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It is like water in a hose. If the hose is full of water, water flows out the end immediately when you turn on the faucet. A drop of water at the faucet pushes a drop next to it, which pushes the next drop. Water doesn't flow that fast. If the hose is empty, it takes a while to reach the end.


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Neutral is a circuit conductor that normally carries current back to the source, and is connected to ground (earth) at the main electrical panel. In the electrical trade, the conductor of a 2-wire circuit connected to the supply neutral point and earth ground is referred to as the "neutral". A difference can occur when either current is flowing down the ...


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the ratio of the change in an electric charge in a system to the corresponding change in its electric potential is called capacitance I.e the ability of system to store charge. You can find more info here. https://en.m.wikipedia.org/wiki/Capacitance


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Because an LED acts like a diode, the negative current from the AC source will be clipped and the capacitor will always be charged and it will act like a second voltage source. Look at my picture below. You can see that the green line represents the voltage going through the capacitor and the blue line (it's a little hard to see since it's covered up by the ...


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The regular spacing and sheer amount of holes in that image is a bit unusual, but I nevertheless suspect that most or all of them are vias: holes drilled through multiple layers of the PCB and plated with copper on the inside to provide an electrical connection between layers. A large number of regularly spaced vias in contiguous planes may be used to spread ...


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Capacitors connected in series $$\frac{1}{C_{\mathrm{total}}} = \frac{1}{C_1} + \frac{1}{C_2}$$ (Where $C$ is the capacitance) Capacitors in parallel $$ C_{\mathrm{total}} = C_1 + C_2$$ As you can see, capacitors are total opposite of resistors when connected in series or parallel More capacitance or $C$ means the capacitor can store more charge. As ...


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There are some small losses, but for saving electricity, turning off the appliances when not in use on a massive scale can be a great help for saving electricity.


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The general notions, to wit, recirculation and highly frequency-selective amplification of noise, carry over almost exactly from electronic oscillators to lasers. From 30 year old memory of electronic oscillators, though, I think some of the details of the dynamical equations are a little different. Also, recirculating a light beam is much more complicated ...


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Resistance can be interpreted in various ways depending on the circuit. It can be used to cause a potential drop, or it can be used as a heating device, etc. You are asking how resistance can change the current flowing through the circuit when connected in series. In that context, the resistance can be used to alter the total resistance of the circuit which ...


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Here is an answer I propose for the 2nd way. I'm for sorry for the bad paintings.


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Your error is to assume that only your red charges generate the heat, ie the red charges go through area $A$ and they are not replaced by any other charges. If that were the case then the factor of $\frac 12$ would be correct. However as the red charges move through the resistor black charges to the left of the red charges would move into the resistor and ...


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Since you equate $W$ with $NqU$, that means $W$ represents the amount of energy dissipated as heat during the time interval $N$ charges passed through the cross section. That time interval is $t / 2$, so the resulting power is $P = {{UIt / 2} \over {t / 2}} = UI$.


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All of the AC motors will create a "back pressure" once power has been removed. I do however not believe you when you say you have a properly grounded piece of equipment. Please note...the grounding system must be complete ALL The way back to a earth ground (grounding rod ect)...grounding cables can have a tendency to create a thin film of oxidation on ...


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RMS means square mean root . i.e. take square add and take mean then take square root. If you take square of ac i.e. sinusoidal waveform the parts from $0$ to $\pi$ become identical to the part between $\pi$ to $2.\pi$. Hence if you add from $0$ to $n.\pi$ and divide by n you will essentially left with one lobe. That's why you can only use one lobe to get ...


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For devices like battery chargers, motors and lamps the fluctuating voltage (ripple voltage) does not really matter but for a device like an audio amplifier the ripple voltage may well manifest itself as a mains hum.


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As long as the circuit is linear you should be able to find a Thevenin equivalent circuit. The next thing to note is that you usually find the equivalent Thevenin circuit for a real circuit in order to evaluate (more easily) what happens in the external circuit which in your case is the $3 \; \Omega$ (load) resistor connected between nodes $a$ and $b$. So ...


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The inductor works the same as it does in AC circuits : the PD across it is related to the current through it by $V = L\frac{dI}{dt}$. You are correct : the current I through L increases in proportion to $1-e^{-kt}$ towards a maximum value. Meanwhile $\frac{dI}{dt}$ decreases from a maximum value to zero. When the maximum current flows it is constant, ...


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It depends on what you have. Sources can be modeled as a current source or a voltage source. If you treat it as a voltage source, it will always output that peak voltage and the circuit current will change according to the resistance changes. If you treat it as a current source, it will always output that peak current and the voltage drop across it will ...


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So shouldn't there already be a drop in voltage ( potential difference) before the charges even reach a resistor? Normally we view a battery or a cell as accumulator of charges in a manner that a potential difference is built up when we charge a battery with plates and electrolyte. Therefore if charges flow out or current is being drawn at certain voltage ...


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I think that you have missed an assumption that is often used in circuit theory and that is that the connecting leads have a negligible resistance. In the real world the leads do have a resistance and so as the (positive) charge moves from the positive terminal of the battery there is a conversion of electric potential energy into heat and the same ...


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Resistive systems are not conservative. This can be seen by the fact that the system experiences a potential drop whichever direction current passes through a resistor. The current is essentially experiencing a drag force which cannot be written as the gradient of a potential function; you can't 'draw' the potential landscape for a resistor, so it won't ...


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If you have a multimeter you can do it easily. Think of the capacitor as three resistors in series: the first lead, the dielectric, and the other lead. Resistors in series add resistance to combine, so we will add those three: $$R_{eq} = 2R_{leads} + R_{dielectric} $$ We can assume the leads to have a resistance of almost 0 since they conducting metals. So ...


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The traditional electric bell uses an electromagnet to move the arm that strikes the bell. Electromagnets require the core to be low coercivity as a high coercivity causes losses due to hysterisis, and iron happens to meet this requirement. There is nice explanation of the effect of coercivity in the answers to Properties to select suitable materials for ...


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When I was studying about electric circuits, I had a similar problem too. But when I discovered where I was going wrong, it made things pretty clear for me. I will share with you what problem I faced, as it may be true that you are facing the same. Current is the quantity of charge passing through the circuit in unit time, by definition. Observe the ...


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The power consumed by your circuit determines how fast the battery drains. P = I * E: power (Watts) is found by multiplying the current (Amps) by the voltage (Volts). Since your battery has a (reasonably) constant voltage under normal operation, current is the variable here. I = E / R, amps = volts / ohms. If we combine these two equations, we get P = E ^ ...


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Look into Kirchoff's current law. It is simply charge conservation. If a current of 2 C/s flows in, then 2 C/s must flow out. Because charge is not accumulated anywhere. Inflow must equal outflow at every single point in a steady circuit. Mathematically: $$\sum I=0 \quad \Leftrightarrow \quad \sum I_{in}-\sum I_{out}=0$$ When you in a series circuit have ...


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The current flows in the wires of a circuit, carried by the movement of electrons. At any particular time, if you measure the current at two different places in the same wire, you will get the same reading. This is Kirchhoff's current law in action: all the current entering a point in a circuit must leave that point. Any point on your wire can be seen as a '...


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There is not such an integral because resistance is a property of whole circuits that may be defined in isolation only in an approximate way. The closest I have come to an integral expression is eq. 63 in https://www.academia.edu/1841457/The_Notion_of_Electrical_Resistance


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As already said, you could just write Kirchhoff's equations assuming you know the voltage between A and B. Imagine you are given a two resistors connected in parallel. Then for a given voltage you can express currents through it and resistances using Ohm's law and charge conservation (this's Kirchhoff's equations). So the current would be proportional to a ...


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I can see why you think physicists might have some insight into such a problem, because of the way it has been presented as an electrical circuit. Unfortunately we have little to add to what the Mathematicians and Computer Scientists can tell you. We certainly have no tricks which they do not already know about. I think this is a mathematical or ...


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Within a source of emf like a battery a chemical reaction occurs which moves the mobile charge carriers from a region where they have low electric potential energy to a region where they have a higher electric potential energy. If the charge carriers are positive that is taking those positive charge carriers from the negative terminal of the battery to ...


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Charge is conserved, so the equation of continuity should be applied, . It states that the divergence of the current density J (in amperes per square meter) is equal to the negative rate of change of the charge density ρ (in coulombs per cubic metre), Current is the flow of electric charge. So if the divergence of J is positive, then more charge is ...


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Long ago somebody decided that the direction of "conventional" current flow was the same direction as the direction of flow of positive charges. In that convention the flow of negative charge in one direction is equivalent to the flow of positive charge (and hence the conventional current) in the opposite direction. When introduced electricity usually ...


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Nothing "flows" actually. Electrons transfer the electrical energy by hitting each other. And even if you consider flowing, only electrons free. Protons cannot because they're held strongly in nucleus. About charge, textbooks usually refers it as positive. That means, we just take the opposite direction of electron flow as +ve charge (because electrons are ...


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I suspect that your confusion is caused by the difference between conventional current and the flow of electrons. Conventionally the direction of a current is the direction in which +ve charges move, and this direction is from higher potential (more +ve) to lower potential (less +ve). However, this convention was chosen historically before we knew what the ...


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The motion of electrons in the wires and the voltages can't be "seen" by naked eyes so the whole science of electric circuits is automatically "harder to visualize" than mechanics. But all such laws and phenomena have mathematically similar analogies in mechanics. The voltage is analogous – not only mathematically but physically – to the slope of an ...


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If you connect a battery to a series of resistors, then you can easily calculate the current flowing through the circuit. If you place a (perfect) voltmeter across a particular resistor $R$ that carries a current $I$ it will measure the p.d. across the resistor as $I \times R$. However, if you place the voltmeter across a piece of wire (with zero resistance) ...



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