The potential defferences across the resistance capacitance and indutance are 80 V, 40 V and 100 V respectively in an L-C-R circuit. The power factor of this circuit is

Options

A. `0.4`
B. `0.5`
C. `0.8`
D. `1.0`

Answer

To find the power factor of the L-C-R circuit given the potential differences across the resistance (R), capacitance (C), and inductance (L), we can follow these steps:

### Step 1: Identify the given values
- Voltage across the resistance (V_R) = 80 V
- Voltage across the capacitance (V_C) = 40 V
- Voltage across the inductance (V_L) = 100 V

### Step 2: Calculate the net voltage across the inductance and capacitance
In an L-C-R circuit, the voltages across the inductance and capacitance are out of phase. Therefore, we can find the effective voltage (V_L - V_C) as follows:
- Effective voltage (V_L - V_C) = V_L - V_C = 100 V - 40 V = 60 V

### Step 3: Construct the voltage triangle
In the voltage triangle:
- The horizontal side represents the voltage across the resistance (V_R).
- The vertical side represents the net voltage across the inductance and capacitance (V_L - V_C).

### Step 4: Calculate the total voltage (V)
Using the Pythagorean theorem, we can find the total voltage (V) in the circuit:
\[ V = \sqrt{V_R^2 + (V_L - V_C)^2} \]
Substituting the values:
\[ V = \sqrt{(80)^2 + (60)^2} \]
\[ V = \sqrt{6400 + 3600} \]
\[ V = \sqrt{10000} \]
\[ V = 100 V \]

### Step 5: Calculate the power factor (PF)
The power factor is defined as the ratio of the voltage across the resistance to the total voltage:
\[ \text{Power Factor (PF)} = \frac{V_R}{V} \]
Substituting the values:
\[ \text{PF} = \frac{80 V}{100 V} = 0.8 \]

### Final Answer
The power factor of the circuit is **0.8**.

---