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If I take a simple piece of conducting wire (of which I can calculate the resistance from the wire dimensions and resistivity of the wire material) and connect it across the terminals of a battery of potential difference V, I can calculate the value of the current from Ohm's Law:

i=V/R, where i is the steady state current.

However, if the cable is long and I need to plot the current against time right from the moment zero, I might have to take into consideration some capacitance and inductance of the circuit.

My question is : Where do the capacitance and inductance come from? Do they come from the loop shape the wire might have taken somewhere along the path and the elemental electric fields that exist inside the wire to drive the flow of charge? Please help with some explanation.

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Capacitance is about stored charge - more electrons flowing into something than flow out. This can happen in a piece of wire, although it can take a large amount of applied voltage to accumulate a small amount of excess electrons. In other words, a simple piece of wire has very low capacitance.

Even a straight piece of wire will have inductance because any current carrying conductor will have a magnetic field, and it is the interaction of electric current and the magnetic field which produces the effect we call inductance. In the case of a straight piece of wire, the magnetic field lines are essentially cylindrical, co-axial with the wire. Inductance in a straight piece of wire is very small; winding around a core increases the effect due to interaction between adjacent windings (and interaction with the core, if made of suitable material).

Even though the capacitive and inductive reactance of a straight piece of wire is very small, the tiny values can become significant at very high frequencies.

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  • $\begingroup$ $$X_C=\frac 1{ωC}$$ By capacitance you are referring to the $X_C$ right? $\endgroup$
    – Shub
    Feb 3 at 17:45
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Where does a straight conducting wire get its capacitance?

Two parallel wires form a long capacitor with cylindrical plates (see Capacitance of Parallel Metal Wires).

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  • $\begingroup$ And, wires also have a capacitive reactance to other nearby conductors such as the earth, other metal, and even people. An antenna wire has capacitive affects with ground that must be taken into account to determine all of the operational parameters and impedances. $\endgroup$
    – K7PEH
    Nov 8, 2015 at 4:07

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