I need to calculate the voltage through the resistor and the voltage through the inductor of an RL series circuit for different frequencies. The voltage of the source is 2.5 V. The inductor is at the top and has an inductance of .200 H and the resistor is at the right with a resistance of 5.1 kilo ohms.
To calculate VR and VL I was going to use VR=Z2/(Z2+Z1) and VL=Z1/(Z2+Z1).
I read that Z for the resistor is equal to R and i don't know what Z for the inductor is. i know that the total Z is sqrt(R^2+w^2L^2) so i don't know if Z for the inductor (or Z1) will be Ztot-ZR.
I want to know if I'm approaching this correctly. What I did for VL when the frequency was 1000 Hz was:
Z2= Ztot-Z1
Z2=3.91
VL= Z2/(Z1+Z2)=1.92 mV.
Am I doing this correctly?
How can the angles for Vr be calculated?
Zi=Xi= j2PIf*L where j is a phasor
R+Xi=5100+j w.200
Now, when you compute that total impedance, notice that it is a complex number.
Z=R+Xl=5100+j6280*.2
mag Z= sqrt (5100^2+1256^2)=5252ohm check that. For the angle, theta=arctan(1256/5100), so I will be at that angle with respect to source voltage.
Now, you have to consider angles on the inductor.
Vl=Z2/(R+Xl) but Z is at 90, and the denominator is at theta, so Vl is at 90-theta.
The angle of Vr is at theta, it is in phase with the current.
Vr and Vl do not add to Vs in magnitude, however, as vectors, they will add to Vs
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.