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What is the relationship and proportionality between current and time in RL circuit when a voltage source is present? (3 points)

a) I∝t
b) I∝ 1/t
​c) I∝t^2
d) I∝e ^−t

User MatlabNewb
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1 Answer

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Final answer:

The current in an RL circuit is proportional to e^{-t}, growing exponentially as it approaches a steady state value when a voltage source is present.

Step-by-step explanation:

The relationship between current (I) and time (t) in an RL (resistor-inductor) circuit when a voltage source is present is characterized by an exponential function. The time variation of the current, after a switch is closed and the circuit is first powered on, can be described by the equation I(t) = Io(1 - e^{-Rt/L}), where I is the current at time t, Io is the maximum current (V/R), R is the resistance, L is the inductance, and e is the base of the natural logarithm. Therefore, the correct answer to the student's question is I∝e^{-t}, indicating the current grows and eventually approaches a steady state over time following an exponential increase.

User IZBasit
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