Aresistor, an inductor, and a switch are all connected in series to an ideal battery of constant terminal voltage. what does the time constant for the circuit represent?

In physics and engineering, the time constant usually denoted by the Greek letter τ, (tau), characterizes the frequency response of a first-order, linear time-invariant (LTI) system. Time constant of an RC circuit is the product of R and C. Time constant of an RL circuit is equal to inductance divided by resistance. 

stands for electromotive force and it is measured in volts. despite its name, it is not actually the force in the sense of being a "pushing" or "pulling" (not measured in newtons).an equation that relates emf,  ℰ,  to a battery's terminal voltage, v, current, i, and internal resistance, r, is    ℰ = v + irin this case, the emf can be interpreted as a voltage—a difference in electric potential.i would not say that it would be considered an energy. if emf can be defined as the energy/work per a unit charge from a battery or other electric source, then it is not strictly energy.