Question

An inductor electromagnet can be modeled as an RL circuit when it is being energized with a voltage source. If the inductance is 13 H and the wire windings contain 29 ohms of resistance, how long does it take a constant applied voltage to energize the magnet to within 92% of its final value (that is, the current equals 92% of its asymptotic value)?

Answer 1

The time it takes for the current to reach 92% of its final value in an RL circuit can be found using the time constant formula τ = L/R and the logarithmic equation t = τ * ln(1 / (1 - 0.92)).

Step-by-step explanation:

To find the time it takes for the current to reach 92% of its final value in an RL circuit, we can use the formula for the time constant, which is given by the equation: τ = L/R, where τ is the time constant, L is the inductance, and R is the resistance. In this case, the inductance is 13 H and the resistance is 29 ohms, so we can substitute these values into the equation to find the time constant: τ = 13 H / 29 ohms = 0.448 s.

The time it takes to reach 92% of the final value can be found by multiplying the time constant by ln(1 / (1 - 0.92)), where ln is the natural logarithm. Using this formula, the time it takes is: t = 0.448 s * ln(1 / (1 - 0.92)) = 2.418 s.

So it takes approximately 2.418 seconds for the current in the RL circuit to reach 92% of its final value.