Final answer:
The current through an inductor in an AC circuit can be calculated using the inductive reactance (XL = 2πfL), the impedance (Z = √(R² + XL²)) of the RL circuit, and Ohm's law (V = IZ). The result is given in complex form (A + jB), which can be converted to polar form for magnitude and phase angle.
Step-by-step explanation:
To calculate the current through the inductor in polar form, we need to use the concept of inductive reactance (XL) and Ohm's law for AC circuits. Inductive reactance is given by XL = 2πfL, where f is the frequency and L is the inductance. The impedance Z in an RL circuit is Z = √(R² + XL²). With the resistance (R) given as 30 kΩ, inductance (L) as 1.5 H, and frequency (f) as 4000 Hz, we can calculate the reactance XL and then impedance Z. To find the current (I), we divide the voltage (V) by the impedance (Z), using Ohm's law V = IZ. The result will be in complex form (A + jB), which can then be converted to polar form to find the magnitude and phase angle of the current.
Firstly, calculate the inductive reactance: XL = 2π(4000)(1.5). Then, calculate the impedance Z = √((30³)² + (XL)²). Lastly, use Ohm's law to find the current: I = V/Z, where V is 12 V. Remember to keep track of your units throughout the calculations.