Questions: RL Circuits

Question 1

A circuit has a 12 V battery, a 4 Ω resistor, and an 8 H inductor in series. The switch is closed at t = 0. What is the current through the circuit immediately after the switch closes?

• A. 3 A — Ohm's law gives I = ε/R = 12/4
• B. 0 A — the inductor prevents any instantaneous change in current
• C. 1.5 A — the inductor acts as a 4 Ω equivalent impedance at t = 0
• D. Undefined — no current flows until the transient ends

Answer: (B)

At t = 0, the inductor's back-EMF exactly cancels the source voltage, so the initial current is zero. The inductor does not block current permanently — it resists instantaneous *changes* in current. The current builds exponentially toward ε/R = 3 A over time. Option A is the steady-state answer, not the t = 0 answer. This is the most common confusion: treating the inductor's initial behavior as a steady-state Ohm's law calculation.

Question 2

What happens to the time constant τ of a series RL circuit if the resistance R is doubled while the inductance L stays the same?

• A. τ doubles, because more resistance means slower current flow
• B. τ halves, because τ = L/R and doubling R reduces τ
• C. τ stays the same, because L is unchanged
• D. τ increases by a factor of 4, because energy dissipation goes as R²

Answer: (B)

The time constant is τ = L/R. Doubling R halves τ, meaning the circuit reaches steady state twice as fast. This is counterintuitive to many students who think more resistance means slower response — but more resistance means more energy dissipated per unit current, which actually drains the transient faster. Compare with RC circuits where τ = RC and larger R *slows* the response: in RL circuits, R plays the opposite role.

Question 3

In an RL circuit at t = 0, the inductor acts like an open circuit because no current can ever flow through an inductor.

• T. True
• F. False

Answer: False

The inductor acts like an open circuit *initially* (at t = 0) only in the sense that it constrains the current to start at zero and change at a finite rate. Current does flow through the inductor — it just cannot change instantaneously. The open-circuit analogy describes the initial state: the back-EMF equals the source voltage, so net current is zero. But current builds continuously after that, and at steady state the inductor acts as a plain wire (short circuit) with no voltage drop at all.

Question 4

Abruptly opening an RL circuit while a large current is flowing can produce a voltage spike much larger than the original source voltage.

• T. True
• F. False

Answer: True

The inductor's voltage is V = L dI/dt. If the circuit is interrupted suddenly — making the current drop from I₀ to zero in a very short time — then dI/dt is enormous, and the inductor produces a correspondingly huge voltage spike. This can arc across switch contacts and destroy semiconductor components. This is why real circuits use snubber (flyback) diodes across inductors: they provide an alternative current path to allow the energy to dissipate safely rather than appearing as a destructive spike.

Question 5

Why does the current in a DC RL circuit approach ε/R at steady state rather than continuing to grow? What role does the inductor play once steady state is reached?

Model answer: At steady state, dI/dt = 0 — the current is no longer changing. Since the inductor's voltage is V_L = L dI/dt, a zero rate of change means the inductor contributes no voltage drop. It behaves as a plain wire (short circuit). With only the resistor left in the circuit, Ohm's law gives I = ε/R. The current doesn't grow indefinitely because as it approaches ε/R, the back-EMF of the inductor decreases, reducing dI/dt, which is the self-limiting exponential approach to equilibrium.

This is the key to understanding inductor behavior in DC circuits: inductors only 'fight back' when current is changing. Once steady state is reached and dI/dt = 0, the inductor is electrically invisible. It becomes relevant again the moment any change is introduced — a switch opened or closed, a load added — at which point it resists the new change and the transient begins again.