Question

An inductor with inductance L resistor with resistance R are wiredin series to an ideal battery with emf ε. A switch in thecircuit is closed at time 0, at which time the current is zero. Along time after the switch is thrown the potential differencesacross the inductor and resistor

A) 0, ε
B) ε/2,ε/2
C) (L/R)ε,(R/L)ε
D) cannot becomputed unless the rate of change of the current is given
E) ε, 0

Answer 1

In a series RL circuit with a battery after a long time, the potential difference across the inductor is zero, and the potential difference across the resistor is equal to the battery's emf.

Step-by-step explanation:

When an inductor with inductance L and a resistor with resistance R are wired in series to an ideal battery with emf ε and the switch is closed at time t = 0, the initial current is zero. Over time, as the current in the RL circuit increases exponentially, it will approach a steady-state value where the potential difference across the inductor will be zero, and the potential difference across the resistor will be equal to the emf of the battery (ε). This is because, in the steady state, the inductor behaves like a short wire and all the voltage drops across the resistor. Therefore, the correct answer is E) ε, 0.