To calculate the voltage across the resistor (VR) and the voltage across the inductor (VL) in an RL series circuit, your approach is correct.
For the resistor, the impedance (Z) is equal to its resistance (R). So, VR will be equal to V * (R / (R + ZL)), where V is the voltage of the source.
For the inductor, the impedance (ZL) depends on both the frequency (f) and the inductance (L). The impedance of an inductor is given by ZL = j * 2 * π * f * L, where j represents the imaginary unit (√(-1)).
To find VL, you will need to calculate ZL using the formula above and then use the equation VL = V * (ZL / (R + ZL)).
Let's use an example to demonstrate:
Given:
V = 2.5 V
R = 5.1 kΩ
L = 0.200 H
f = 1000 Hz
First, let's calculate ZL:
ZL = j * 2 * π * f * L
ZL = j * 2 * π * 1000 * 0.200
ZL = j * 1256
Now, let's calculate VR:
VR = V * (R / (R + ZL))
VR = 2.5 * (5.1 * 10^3 / (5.1 * 10^3 + j * 1256))
VR ≈ 2.480 V
Finally, let's calculate VL:
VL = V * (ZL / (R + ZL))
VL = 2.5 * (j * 1256 / (5.1 * 10^3 + j * 1256))
VL ≈ 0.020 V or 20 mV (Note: Your calculation of 1.92 mV seems incorrect)
To calculate the angles for VR and VL, you can convert the complex numbers to polar form and extract the angle. For example, for VR, you can find the angle (θ) such that VR = |VR| * e^(jθ), where e is the base of the natural logarithm.
I hope this helps! Let me know if you have any further questions.