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Essentially, if I were to plot current against time for a simple circuit with a DC cell and a resistor in it, would there be a non-flat profile from time $t = 0$.

So, between $t = 0$ and $t = t_1$, where $t_1$ is the time at which the current in the circuit reaches a steady state of $i = V/R$, would $$\frac{\partial i}{\partial t} \neq 0$$

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  • $\begingroup$ Welcome to stack exchange! Whilst you have a valid point that there is a slight time delay due to the speed of transfer of energy, in reality it is a tiny tiny delay and would be quite hard to measure $\endgroup$ – Alex Robinson Oct 10 '19 at 15:47
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For calculations, it depends on the features you want to model.

This won't happen in a physical circuit. If you don't want to get to fine detail and start worrying about propagation delays, then the simplest way to avoid it is to look at the inductance.

Any real circuit will have a non-zero inductance. You can think of this as the circuit's mass or inertia. The larger the inductance, the slower the current will change in response to a voltage difference. The inductance will be quite low for a simple wire loop, but still large enough to model.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indtra.html#c1

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  • $\begingroup$ Thanks for the answer. Okay, my question was really a pre-cursor into RL circuits as I'm stuck conceptually on what causes the exponential relationship. What causes the rate of change of current to start high and decrease with time? $\endgroup$ – Jamie Smith Oct 11 '19 at 7:47
  • $\begingroup$ Perhaps physics.stackexchange.com/questions/335777/… ? $\endgroup$ – BowlOfRed Oct 11 '19 at 15:58

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