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. What is the differential equation satisfied by the current I(t) after time t=0? What is the expression for I(t) obtained by solving the differential equation that I(t) satisfies after t=0? What is the time constant τ of this circui
145. 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.
What is the differential equation satisfied by the current I(t) after time t=0?
What is the expression for I(t) obtained by solving the differential equation that I(t) satisfies after t=0?
What is the time constant τ of this circuit?
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