In an AC circuit , current is `3A` and voltage `210V` and power is `63W`. The power factor is

Options

A. (a)0.11
B. (b)0.09
C. (c)0.08
D. (d)`0.10`

Answer

To find the power factor in the given AC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between power, current, voltage, and power factor:**
The power (P) in an AC circuit can be expressed as:
\[ P = V \cdot I \cdot \cos(\theta) \]
where:
- \( P \) = Power in watts (W)
- \( V \) = Voltage in volts (V)
- \( I \) = Current in amperes (A)
- \( \cos(\theta) \) = Power factor

2. **Rearranging the formula to find the power factor:**
We can rearrange the equation to solve for the power factor:
\[ \cos(\theta) = \frac{P}{V \cdot I} \]

3. **Substituting the given values:**
We have:
- Current \( I = 3 \, \text{A} \)
- Voltage \( V = 210 \, \text{V} \)
- Power \( P = 63 \, \text{W} \)

Plugging these values into the formula gives:
\[ \cos(\theta) = \frac{63}{210 \cdot 3} \]

4. **Calculating the denominator:**
First, calculate \( V \cdot I \):
\[ V \cdot I = 210 \cdot 3 = 630 \]

5. **Calculating the power factor:**
Now substitute back into the power factor formula:
\[ \cos(\theta) = \frac{63}{630} \]

6. **Simplifying the fraction:**
\[ \cos(\theta) = \frac{63 \div 63}{630 \div 63} = \frac{1}{10} = 0.1 \]

7. **Conclusion:**
The power factor is \( 0.1 \).

### Final Answer:
The power factor is \( 0.1 \).