The Switch in the Circuit Shown Below Has Been Closed $= 0$

question 4

Essay

the switch in the circuit shown below has been closed for a long time before it is opened at t $= 0$ . Find the current $i ( t )$ through the inductor for $t \geq 0$ . Assume $R _ { 1 } = 3 \mathrm { k } \Omega , R _ { 2 } = 1 \mathrm { k } \Omega , I _ { s } = 2 \mathrm {~mA}$ , $\mathrm { L } = 120 \mathrm { mH }$ .

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Definitions:

Existential Instantiation

A logical rule asserting that if an existential statement is true, there is at least one specific instance of its subject that satisfies its predicate.

Universal Instantiation

A logical rule that allows for the deduction of a particular instance of a statement from a universal statement.

Existential Generalization

A logical operation that infers the existence of at least one individual satisfying a certain property from a specific instance.

Quantifier Negation

The process of applying negation to a quantified statement, potentially altering its meaning significantly.