The analogy “electric current as water flowing in a pipe” is useful and we will use it often: the battery is the pump, the resistance is the narrowing of the pipe, the current is the water flow, the voltage is the pressure difference. Many intuitions about circuits arise from this and will accompany us throughout the study. But every analogy is a bridge, and this one breaks at least at two fundamental points.
First limit — the charges are already there. The electric current is not a jet of water arriving from far away: the charges (the electrons) are already present inside the conductors. When you close the circuit they all start moving together, almost instantaneously, because it is the electric field that propagates — at the speed of light — telling every electron “go now”. There is no filling-up time for the pipe.
Second limit — resistance is not friction. There is no “friction” in the mechanical sense. Resistance is a statistical phenomenon of collisions between the electrons and the crystal lattice, and at low temperatures it can disappear entirely: this is superconductivity, unthinkable for the friction of a fluid in a pipe.
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Every analogy is a bridge: it works until you try to carry a machine too heavy across it (Arons 1997; Battimelli and Stilli 1999).
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Topics: Electric circuits Skills: Analysis of limiting cases and thought experiments
Related exercises: Worked exercise — mixed series-parallel network · Worked exercise — capacitor network · Worked exercise — charging RC circuit