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

Options

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

Explanation

To find the power factor of the given L-C-R circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given voltages**:
- Voltage across resistance (Vr) = 80 V
- Voltage across capacitance (Vc) = 40 V
- Voltage across inductance (Vl) = 100 V

2. **Understand the phase relationships**:
- The voltage across the resistor (Vr) is in phase with the current (I).
- The voltage across the inductor (Vl) leads the current by 90 degrees.
- The voltage across the capacitor (Vc) lags the current by 90 degrees.

3. **Represent the voltages in a phasor diagram**:
- Draw Vr horizontally to the right (as it is in phase with I).
- Draw Vl vertically upwards (as it leads the current).
- Draw Vc vertically downwards (as it lags the current).

4. **Calculate the net reactive voltage**:
- Since Vl and Vc are in opposite directions, we can subtract them:
\[ V_{net} = V_l - V_c = 100 V - 40 V = 60 V \]

5. **Determine the total voltage (V)**:
- The total voltage (V) in the circuit can be represented as:
\[ V = \sqrt{V_r^2 + V_{net}^2} \]
- Substitute the values:
\[ V = \sqrt{(80 V)^2 + (60 V)^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 V \]

6. **Calculate the power factor (cos φ)**:
- The power factor is given by:
\[ \cos φ = \frac{V_r}{V} \]
- Substitute the values:
\[ \cos φ = \frac{80 V}{100 V} = 0.8 \]

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

---