We would like to use the relation v(t)=i(t)r to find the voltage and current in the circuit as functions of time. to do so, we use the fact that current can be expressed in terms of the voltage. this will produce a differential equation relating the voltage v(t) to its derivative. rewrite the right-hand side of this relation, replacing i(t) with an expression involving the time derivative of the voltage. express your answer in terms of dv(t)/dt and quantities given in the problem introduction.

Yes

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.