Question

Calculate the reactance of a 2-H inductor at frequency of 10 Hz. Hint: Provide only the numerical answer in decimal format. What is the phase in degrees of the current through a 20-mH inductor when the applied voltage across its terminals is u(t) = 48 cos(377t + 20°) V? Hint: Provide only the numerical answer in decimal format.

Answer 1

The reactance of a 2-H inductor at a frequency of 10 Hz is approximately 125.66 ohms. The phase in degrees of the current through a 20-mH inductor when the applied voltage across its terminals is u(t) = 48 cos(377t + 20°) V is also 20°.

Step-by-step explanation:

To calculate the reactance of an inductor, we use the formula XL = 2πfL, where XL is the reactance, f is the frequency in hertz, and L is the inductance in henries. Given that the inductance is 2 H and the frequency is 10 Hz, we can substitute these values into the formula:

XL = 2π(10)(2) = 40π ≈ 125.66 ohms.

To calculate the phase of the current through the inductor, we need to find the phase angle of the voltage. In the given equation, u(t) = 48 cos(377t + 20°) V, the phase angle is 20°. Therefore, the phase angle of the current through the inductor is also 20°.