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.

ENGR-217:201,202,203,204,501,502,505,506,515,516,521,522,523,524,525,526,535,536,PHYS-217:203,204,501,502,503,531,532,533 Final Exam

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:

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