Question

how is current defined dQ/dt=0,how can a current if dq/dt=0.

Answer 1

Current is basically the rate of change of charge with time. 'dq' represents the rate of change of charge and 'dt' represents the change of time. for example if 5 Coulombs of charge is flowing through a wire in 1 second,then we say current is 5 Amperes.

Answer 2

there can not be current in the circuit if dq/dt=0...... 'cause it is basically the rate of charge flow

Answer 3

What that actually implies to me is that the circuit is impedance free since there is no change in the electron count Q over a given change in time. This is most easily obtained with a DC source; and is achieved when the flow into the "components(s)" being defined is not changing. The two impedance producers are: 1) capacitance, and 2) inductance. A capacitor fills up, and the flow rate drops, and then stops when the potential in it matches the source. When thus matched, it can be defined, ideally, as an open circuit; though in most cases for large capacitors there is a very high resistance in its characteristics. After applying a DC source to the inductor though, it loses it change in magnetic flux (that generates as a reverse voltage in it internally) as the current flowing through it persists at nearly the same rate. Once stabilized, it can be defined as a simple resistor. When one has an AC source supplying power to components, especially at high frequencies, then the “delta (change in) Q per delta (change in) time” no longer can exist as 0, as even simple wires have inductance and capacitance. Luckily one can use one effect to balance out the other to a large degree, but usually only at one frequency

Answer 4

Maybe there's a confusion between
1) the requirement that dQ/dt must be zero for each component for the lumped parameter abstraction to be satisfied, and
2) the definition that current = dq/dt?

If that's it, the difference is the way q is being defined. In the first case, Q refers to the net number of charge carriers in the circuit. The boundary is a CLOSED surface, like a ziplock surrounding the component or circuit. In the water analogy to charge, it's a closed system; the water can flow around, but if a liter of water enters a component in a second, a liter must exit it too. (That's true, by the way, for capacitors too, even though they're often confusingly called "charge storage devices").

In the second case, q refers to just the number of charge carriers entering a component. It is an open boundary with edges, like a sheet of paper placed through a wire. So you can have (with the water analogy to charge carriers) a liter of water per second entering a pipe restriction, just like you can have a coulomb of charge per second entering a resistor.

Answer 5

@junglejim If one desires something more common to make an analogy with for electricity's ways; I've come to lean on air and plumbing. An air tank represents a capacitor that can be charged to different densities of air molocules. The resistor is obviously any type of restriction, which the plumbing itself has as least some small amount. The hardest to parallel is the inductance. It is like a flywheel connected to a very efficient turbine (perhaps designed like a vacuum cleaner's). When it first receives flow it is resistant to it until the flywheel get up to speed. After the source stops supplying current to it, the flywheel keeps pushing more current, even if this causes the pressure to rise very high. This is essentially how a coil in a car engine generates a high voltage spark from its battery's voltage; though it does effectively use a transformer arrangement to make the voltage even higher. Which is effectively like adding 'still tight' low flow vane turbine to the same flywheel. Note how a vaccuum cleaner's engine gets a low (ideally no) load when there is no air given to it to flow. The delta Q business to me defines the conditions they are quantifying the components characterist in. You may note that inductance is seldom (if ever) a specification supplied for those components; and at the sizes used for microchips circuits, it is nearly non-existent anyway. Transistors and other discrete semiconductor 'parts' are like air controlled valves and switches. Transistors are somewhat tied to flow ratios, FETs and others are more pressure actuated and loaded to be in various states of resistance when not being triggered or controlled. The SCR and TRIAC locks on when triggered until the flow is stopped or reversed. Beyond that is sensors or transducers and mainly the arrangements of such parts that have notable behaviors.

Answer 6

@ gdmellott, that's pretty cool! I like both models...hydraulics because that model's capacitor (a rubber sheet across a pipe) keeps the divergence of the charge = 0 unlike the air storage tank, and its pretty intuitive to see how high frequency is passed through a cap (the rubber sheet doesn't have time to flex much, so always low pressure difference) and DC is blocked. Inductance is a bit easier too with the weight of the water...everyone who's lived in a city knows the water hammer sound from turning off a faucet too rapidly and seeing what happens in an inductor when you shut off flow too quickly (and solve it with a capacitor...using your model of an air pocket!). For FET and BJT behavior, I agree that pneumatic pressure and flow switches are more intuitive than water.