Consider a purely inductive ac circuit in which the maximum voltage across the inductor is Vmax=98.0V. If the maximum current is 7.40A at 40.0Hz, what is the inductance L? Answer in mH.
To find the inductance L of the purely inductive AC circuit, we can use the formula:
Vmax = L * (2 * π * f) * Imax
Where:
Vmax is the maximum voltage across the inductor,
L is the inductance,
f is the frequency of the AC circuit, and
Imax is the maximum current.
We are given:
Vmax = 98.0V,
Imax = 7.40A,
f = 40.0Hz.
Substituting the given values into the formula, we have:
98.0V = L * (2 * π * 40.0Hz) * 7.40A
To solve for L, we rearrange the formula:
L = Vmax / (2 * π * f * Imax)
Substituting the given values into the rearranged formula, we get:
L = 98.0V / (2 * π * 40.0Hz * 7.40A)
Calculating this expression will give us the value of inductance L in the appropriate units.
Please note: In the final step, make sure to keep track of the units so that the answer is given in millihenries (mH) as requested.