Final answer:
The time it takes for an RL circuit to reach 75% of its maximum current value can be found using the equation for the current in an RL circuit. For the given RL circuit with R=28.68Ω and L=75.11mH, it takes approximately 1.081 ms for the current to reach 75% of its maximum value.
Step-by-step explanation:
To find the time it takes for an RL circuit to reach 75% of its maximum current value, we can use the equation for the current in an RL circuit:
I(t) = I0(1 - e-t/τ)
where I(t) is the current at time t, I0 is the maximum current, t is the time, and τ is the time constant given by τ = L/R, where L is the inductance and R is the resistance.
Given R = 28.68 Ω and L = 75.11 mH, the time constant τ = L/R = 75.11 mH / 28.68 Ω = 2.619 ms. Now, to find the time it takes for the current to reach 75% of its maximum value, we can substitute I(t) = 0.75I0 into the equation and solve for t:
0.75I0 = I0(1 - e-t/2.619 ms)
Cancelling out I0 and rearranging the equation, we get:
0.25 = e-t/2.619 ms
Taking the natural logarithm of both sides, we can solve for t:
ln(0.25) = -t/2.619 ms
Solving for t, we get:
t = -2.619 ms * ln(0.25)
Calculating this expression, we find that it takes approximately 1.081 ms for the current in the RL circuit to reach 75% of its maximum value.