An emf source is used in an RL circuit until steady state current is established.

Then at a time instant t = 0, the emf source is removed from the circuit while keeping continuity in the RL circuit.

Considering the time after instant t = 0, select all that apply:

Question

An emf source is used in an RL circuit until steady state current is established.

Then at a time instant t = 0, the emf source is removed from the circuit while keeping continuity in the RL circuit.

Considering the time after instant t = 0, select all that apply:

BlackTom AI · Accepted Answer

In this RL circuit scenario after removing the source at t = 0, the inductor current cannot change instantaneously and the circuit responds with a natural decay governed by i(t) = I0 e^{-Rt/L}. This implies that the current in the circuit decays exponentially as time progresses.

Option 1: Energy in the inductor causes an oscillatory voltage across the resistor. This is not correct because an RL circuit with only a resistor and inductor (no capacitor) does not support oscillations. There is no restoring force to create a sinusoidal or any oscillatory behavior; the energy stored in the inductor dissipates through the resistor in an exponential fashion.

Option 2: Current decays exponentially. This is correct. Once the source is removed, the inductor current decays according to i(t) = I0 e^{-Rt/L}, which is an exponential decay due to the RL time constant.

Option 3: Voltage decays exponentially. This is correct as well. The voltage across the resistor is v_R = i(t) R, so since i(t) decays exponentially, v_R also decays exponentially with the same time constant, yielding an exponential decrease in the observed voltage.

Option 4: Energy in the inductor causes an exponential decay of voltage oscillations. This statement mischaracterizes the behavior: there are no voltage oscillations to decay, and the energy in the inductor decays monotonically as i^2(t) decreases; there is no oscillatory decay of voltage in this simple RL loop.

Option 5: Energy in the inductor causes an exponential decay of oscillatory current. This is incorrect because the current is not oscillatory in an RL circuit without a capacitive element or driving source; the current simply decays exponentially, not in an oscillatory manner, so there is no exponential decay of an oscillatory current.

Option 6: Energy in the inductor causes an oscillatory current in the circuit. This is false for the same reason: the circuit lacks a mechanism (such as a capacitor) to support oscillations; the current decays smoothly without oscillations, so there is no oscillatory current to decay.

An emf source is used in an RL circuit until steady state current is established. Then at a time instant t = 0, the emf source is removed from the circuit while keeping continuity in the RL circuit. Considering the time after instant t = 0, select all that apply:多项选择题

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