Question

A coil with a resistance of 25ohms and inductance of 0,19H is connected in series with a capacitor of 125×10-6
Voltage supposed 200V with a frequency of 50hz.
Calculate:
A) impedance
B) total current
C) Voltage across the coil
D) Voltage across the capacitor

Answer 1

To solve this problem, we need to calculate a few values related to the RLC circuit consisting of a resistor (coil), inductor, and capacitor connected in series.

### Given Data
- Resistance \( R = 25 \, \Omega \)
- Inductance \( L = 0.19 \, H \)
- Capacitance \( C = 125 \times 10^{-6} \, F \)
- Voltage \( V = 200 \, V \)
- Frequency \( f = 50 \, Hz \)

### Formulas
1. **Angular frequency \( \omega \)**:
\[
\omega = 2\pi f
\]
2. **Inductive reactance \( X_L \)**:
\[
X_L = \omega L
\]
3. **Capacitive reactance \( X_C \)**:
\[
X_C = \frac{1}{\omega C}
\]
4. **Impedance \( Z \)**:
\[
Z = \sqrt{R^2 + (X_L - X_C)^2}
\]
5. **Total current \( I \)**:
\[
I = \frac{V}{Z}
\]
6. **Voltage across the coil \( V_R \)**:
\[
V_R = I \cdot R
\]
7. **Voltage across the capacitor \( V_C \)**:
\[
V_C = I \cdot X_C
\]

### Step-by-Step Calculation

#### A) Impedance Calculation
1. Calculate \( \omega \):
\[
\omega = 2 \pi (50) \approx 314.16 \, rad/s
\]

2. Calculate \( X_L \):
\[
X_L = \omega L = 314.16 \times 0.19 \approx 59.68 \, \Omega
\]

3. Calculate \( X_C \):
\[
X_C = \frac{1}{\omega C} = \frac{1}{314.16 \times 125 \times 10^{-6}} \approx 25.37 \, \Omega
\]

4. Calculate \( Z \):
\[
Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{(25)^2 + (59.68 - 25.37)^2}
\]
\[
Z = \sqrt{625 + (34.31)^2} = \sqrt{625 + 1175.80} \approx \sqrt{1800.80} \approx 42.43 \, \Omega
\]

#### B) Total Current Calculation
\[
I = \frac{V}{Z} = \frac{200}{42.43} \approx 4.71 \, A
\]

#### C) Voltage Across the Coil Calculation
\[
V_R = I \cdot R = 4.71 \cdot 25 \approx 117.75 \, V
\]

#### D) Voltage Across the Capacitor Calculation
\[
V_C = I \cdot X_C = 4.71 \cdot 25.37 \approx 119.44 \, V
\]

### Summary of Results
- **A)** Impedance \( Z \approx 42.43 \, \Omega \)
- **B)** Total current \( I \approx 4.71 \, A \)
- **C)** Voltage across the coil \( V_R \approx 117.75 \, V \)
- **D)** Voltage across the capacitor \( V_C \approx 119.44 \, V \)

These calculations confirm the behavior of the RLC series circuit under the given conditions.