Final answer:
To find the time required for the current through the inductor to be reduced to 0.100% of its original value, we can use the formula for the current through an RL circuit. Plug in the values of the inductance and resistance to calculate the time constant. Set up the equation using the given values and solve for time.
Step-by-step explanation:
To find the time required for the current through the inductor to be reduced to 0.100% of its original value, we can use the formula for the current through an inductor in an RL circuit:
I(t) = I0 * e^(-t/τ)
Where I(t) is the current at time t, I0 is the initial current, e is the base of the natural logarithm, t is the time, and τ is the time constant given by the formula τ = L/R.
Substituting the given values of L = 2.00 H and R = 0.500 Ω into the formula, we have:
τ = 2.00 H / 0.500 Ω = 4.00 seconds
Next, plug the values of I(t) = 0.001 * I0 (0.100% of I0) and τ into the equation and solve for t:
0.001 * I0 = I0 * e^(-t/4.00)
Simplifying the equation, we get:
e^(-t/4.00) = 0.001
Taking the natural logarithm of both sides, we get:
-t/4.00 = ln(0.001)
Finally, solving for t:
t = -4.00 * ln(0.001) = 18.42 seconds
Therefore, the time required for the current through the inductor to be reduced to 0.100% of its original value is approximately 18.42 seconds (option b).