Question

Learning Goal: To understand the mathematics of current decay in an L-R circuit
A DC voltage source is connected to a resistor of resistance R and an inductor with inductance L, forming the circuit shown in the figure. For a long time before t=0, the switch has been in the position shown, so that a current I₀ has been built up in the circuit by the voltage source. At t=0 the switch is thrown to remove the voltage source from the circuit. This problem concerns the behavior of the current I(t) through the inductor and the voltage V(t) across the inductor at time t after t=0

Part A

After t=0, what happens to the voltage V(t) across the inductor and the current I(t) through the inductor relative to their values prior to t=0?

changes slowly and changes abruptly. changes slowly and changes abruptly. Both change slowly. Both change abruptly.

Answer 1

Part A
I changes slowly and V changes abruptly

Part C
= $I_{0}{exp}left(-Rt/Lright)$

Answer 2

There is also a part D to this question

What is the time constant τ of this circuit?

τ = L/R