A student constructs a circuit consisting of an ideal battery of emf \(\varepsilon\), a resistor \(R\), and a slow-start current-limiting component connected in series with an open switch. At time \(t = 0\), the switch is closed, and the current in the circuit begins to increase continuously toward a steady-state value. Which of the following claims and justifications correctly describes the sum of the potential differences around the closed loop at any instant \(t > 0\)?