At what angular frequency will a 12.7-μF capacitor have a reactance XC = 187 Ω𝑋C = 187 Ω ?   rad/s

The reactance (Xc) of a capacitor is given by the formula:

Xc = 1 / (2πfC)

Where: Xc is the reactance, f is the frequency, C is the capacitance.

We can rearrange this formula to solve for the frequency (f):

f = 1 / (2πXcC)

Given that Xc = 187 Ω and C = 12.7 μF (which is 12.7 x 10^-6 F), we can substitute these values into the formula:

f = 1 / (2π * 187 Ω * 12.7 x 10^-6 F)

Solving this will give us the frequency in Hz. However, the question asks for the angular frequency, which is given by ω = 2πf. Therefore, we can simplify our calculation by cancelling out the 2π in the formula:

ω = 1 / (187 Ω * 12.7 x 10^-6 F)

Solving this will give us the angular frequency in rad/s.