Question

Determine i(t) for t > 0 in the circuit of fig. 8.96.

a. This question cannot be answered without the circuit diagram
b. i(t) is constant for t > 0
c. i(t) oscillates indefinitely
d. i(t) decays to zero as t increases

Answer 1

In the given circuit, the current decays to zero as time increases, determined by the circuit's time constant.

Step-by-step explanation:

In the given circuit, the current is not constant for t > 0. Instead, the current i(t) decays to zero as t increases.

The decay of the current is described by a first-order differential equation. The time constant of the circuit, denoted by T, determines how rapidly the current decreases to zero. The current at any time t > 0 can be calculated using the equation i(t) = I0 e-t/T, where I0 is the initial current and e is the base of the natural logarithm.

As t approaches infinity, the current approaches zero. So, option (d) is the correct answer.