An arc lamp consumes `10 A` at `40 V`. Calculate the power factor when it is connected with a suitable value of choke coil required to run the arc lamp on `AC` mains of `200 V ("rms")` and `50 Hz`.

Explanation

To solve the problem step by step, we need to calculate the power factor of the arc lamp when connected to an AC mains supply. Here’s how we can do it:

### Step 1: Identify the given values
- Current (I) = 10 A
- Voltage across the lamp (V) = 40 V
- AC mains voltage (V_rms) = 200 V
- Frequency (f) = 50 Hz

### Step 2: Calculate the impedance (Z)
The impedance (Z) can be calculated using the formula:
\[ Z = \frac{V_{rms}}{I_{rms}} \]
Substituting the known values:
\[ Z = \frac{200 \, \text{V}}{10 \, \text{A}} = 20 \, \Omega \]

### Step 3: Calculate the resistance (R)
The resistance (R) of the arc lamp can be calculated using the formula:
\[ R = \frac{V}{I} \]
Substituting the known values:
\[ R = \frac{40 \, \text{V}}{10 \, \text{A}} = 4 \, \Omega \]

### Step 4: Calculate the power factor (cos φ)
The power factor (cos φ) is given by the ratio of resistance to impedance:
\[ \cos φ = \frac{R}{Z} \]
Substituting the values we calculated:
\[ \cos φ = \frac{4 \, \Omega}{20 \, \Omega} = 0.2 \]

### Final Answer
The power factor when the arc lamp is connected to the AC mains is **0.2**.

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