Question

A 120-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.4 henry and the resistance os 40 ohms. Find the i(t) if i(0)=0. Determine the current as t goes in infinity.

Answer 1

In an LR-series circuit with an applied electromotive force of 120 volts, an inductance of 0.4 henry, and a resistance of 40 ohms, the current is zero for all times t. As t goes to infinity, the current approaches zero as well, reaching a steady state of zero.

Step-by-step explanation:

In an LR-series circuit, the current is given by the equation:
i(t) = I0 * (1 - e-t/(L/R))

Where:
i(t) is the current at time t
I0 is the initial current at t = 0
L/R is the time constant of the circuit, defined as the inductance divided by the resistance

In this case, with an applied electromotive force of 120 volts, an inductance of 0.4 henry, and a resistance of 40 ohms, the time constant is:
L/R = 0.4/40 = 0.01 seconds

For i(0) = 0, we have:
i(0) = I0 * (1 - e0) = 0

Solving for I0, we find:
I0 = 0 / (1 - e0) = 0

Therefore, the current in the circuit is zero for all times t.

As t goes to infinity, the term e-t/(L/R) approaches zero, so the current approaches zero as well. The current in the circuit will eventually reach a steady state of zero.