To calculate the voltage readings across the capacitor and inductor in a series RL circuit with an AC power source, you can use the following formulas:
1. For the voltage across the capacitor (Vc):
Vc = Vrms * (1 / jωC)
Where:
- Vrms is the root mean square voltage of the AC source, which is 25 V in this case.
- ω (omega) is the angular frequency, which can be calculated as 2π times the frequency (f).
ω = 2π * 1000 Hz = 2000π rad/s
- C is the capacitance, which is 0.5 μF or 5x10^-7 F.
Now, plug in these values into the formula:
Vc = 25 V * (1 / (j * 2000π * 5x10^-7 F))
2. For the voltage across the inductor (VL):
VL = Vrms * (jωL)
Where:
- Vrms is again 25 V.
- ω (omega) is the same as calculated before, 2000π rad/s.
- L is the inductance, which is 0.050 H.
Now, plug in these values into the formula:
VL = 25 V * (j * 2000π * 0.050 H)
You can calculate these values to get the voltage readings across the capacitor and inductor. The 'j' in these formulas represents the imaginary unit.
Note that the actual voltage readings will be complex numbers because of the phase difference between the current and voltage in the capacitor and inductor. If you want to find the magnitudes and phases of these voltages, you'll need to perform complex number calculations.