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?
The current flows THROUGH the resistor.
The voltage is ACROSS the resistor.
R = 5.1k Ohms = 5100 Ohms.
L = 0.20 H.
Xl = 2pi*F*L = 6.28 * 1000 * 0.20 = 1256 Ohms = = The inductive reactance.
Z = R + jXl = sqrt(R^2+Xl^2)=The circuit impedance.
Z = sqrt((5100)^2+(1256)^2)=5,252 Ohms.
I = V/Z = 2.5 / 5252 = 4.76*10^-4 Amps.
VR = I*R = 4.76*10^-4 * 5100 = 2.43 Volts.
VL = I*Xl = 4.76*10^-4 * 1256 = 0.598
Volts.
CHECK: E = sqrt(VR^2+VL^2).
E=sqrt((2.43)^2+(0.598)^2)=2.50 Volts.
NOTE: We calculated the vector sum of VR and VL.
Phase Shift Angle:
tanA = Xi/R = 1256 / 5100 = 0.24627.
A = 13.84 Deg.
To calculate the voltage across the resistor (VR) and the voltage across the inductor (VL) in an RL series circuit for different frequencies, you're on the right track by using the impedance equation VR = Z2 / (Z2 + Z1) and VL = Z1 / (Z2 + Z1). Let's break down the approach step by step:
1. Recognizing the components:
- The resistor has a resistance of 5.1 kilo ohms, denoted as R.
- The inductor has an inductance of 0.200 H, denoted as L.
2. Determining the total impedance:
- The total impedance (Ztot) for an RL series circuit is given by Ztot = √(R^2 + (ωL)^2), where ω = 2πf (angular frequency) and f is the frequency. So, you need to calculate ωL for each frequency.
3. Calculating the impedance for the resistor:
- The impedance for the resistor is equal to the resistance itself, so ZR = R.
4. Calculating the impedance for the inductor:
- The impedance for the inductor is given by Z1 = √(Ztot^2 - ZR^2) since Z1 = Ztot - ZR.
5. Calculating the voltage across the resistor:
- Using the equation VR = Z2 / (Z2 + Z1) and substituting ZR = R, you can solve for VR.
6. Calculating the voltage across the inductor:
- Using the equation VL = Z1 / (Z2 + Z1), you can solve for VL.
Now, let's address your specific example where the frequency is 1000 Hz:
You correctly calculated ZR = 5.1 kilo ohms.
To calculate Z1, use Z1 = √(Ztot^2 - ZR^2).
For Ztot:
- Calculate ω by multiplying the frequency (1000 Hz) by 2π.
- Calculate ωL by multiplying ω by the inductance (0.200 H).
- Substitute the values into Ztot = √(R^2 + (ωL)^2) to find Ztot.
Then, calculate Z1 by using Z1 = √(Ztot^2 - ZR^2).
After finding Z1 and ZR, you can calculate VR = Z2 / (Z2 + Z1) and VL = Z1 / (Z2 + Z1) for the specific frequency of 1000 Hz.
Regarding the angles for VR, you'll need to use complex numbers and phasor notation to account for the phase shift. The angle of VR can be calculated as the arc tangent of the imaginary part divided by the real part of VR (angle(VR) = atan(Imaginary part / Real part)). However, since your question did not mention any phase information or reactance values, it seems this might not be necessary in your specific case.
Remember to follow the steps accurately, and use the correct units (e.g., convert kilo ohms to ohms if necessary) to obtain accurate results for VR and VL.