In Fundamentals of Physics (HRW), an equation is derived for the current in a circuit in terms of its emf and resistance by the 'Energy method'; that is, deriving $\epsilon = i \cdot r$ and saying that the work done per unit charge ($\epsilon$) by the (ideal) battery is equal to the thermal energy dissipated per unit charge (i.r).
We know that the (ideal) battery will pump charges with the same emf and do the same work on the charges if or if not the resistor is in the circuit. So if the resistor is not in the circuit, where will the work done by the battery go if there is no resistive dissipation ? In other words, what will happen to the battery if its ends are connected across a super conducting wire ? Will it discharge like a capacitor ?If not, please tell me why the electrical circuit theory is meaningless without resistance.
Many teachers give an analogy between electric circuits and fluid flow in a circuit consisting of pipes and a motor as a battery. If possible, can anyone give me such an analogy with a circuit with zero resistance, internal and external ?
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