The formulas to calculate the capacitive reactance, currents, total current, and phase angle in an RC parallel circuit are:
\[ X_C = \frac{1}{\omega C} \]
Where \(\omega = 2\pi f\)
\[ I_R = \frac{U}{R} \]
\[ I_C = \frac{U}{X_C} \]
\[ I = \sqrt{I_R^2 + I_C^2} \]
\[ \tan \phi = \frac{I_C}{I_R} \]
\[ \phi = \arctan \left( \frac{I_C}{I_R} \right) \]
Where:
An RC parallel circuit is a circuit containing a resistor and a capacitor connected in parallel. The total current in the circuit is the vector sum of the currents through the resistor and the capacitor. The phase angle indicates the phase difference between the total current and the voltage.
Let's assume the following values:
Step 1: Calculate the capacitive reactance:
\[ X_C = \frac{1}{2\pi \times 2300 \times 68 \times 10^{-9}} = 1.02 \, k\Omega \]
Step 2: Calculate the current through the resistor:
\[ I_R = \frac{3.4}{1000} = 0.0034 \, A = 3.4 \, mA \]
Step 3: Calculate the current through the capacitor:
\[ I_C = \frac{3.4}{1.02 \times 10^3} = 0.00334 \, A = 3.34 \, mA \]
Step 4: Calculate the total current:
\[ I = \sqrt{(3.4 \, mA)^2 + (3.34 \, mA)^2} = \sqrt{11.56 + 11.16} = \sqrt{22.72} \approx 4.77 \, mA \]
Step 5: Calculate the phase angle:
\[ \tan \phi = \frac{3.34}{3.4} \approx 0.982 \]
\[ \phi = \arctan(0.982) \approx 44.75^\circ \]