The power factor of an a.c. circuit is givne by `cos phi =`

Options

A. `(R )/(Z)`
B. `(Z)/(R )`
C. `(R )/(X_(L))`
D. `(R )/(X_(C ))`

Answer

To solve the question regarding the power factor of an AC circuit, we need to understand the relationship between the resistance (R), impedance (Z), and the power factor (cos φ).

### Step-by-Step Solution:

1. **Understanding Power Factor**:
The power factor (PF) of an AC circuit is defined as the cosine of the phase angle (φ) between the voltage and the current. It indicates how effectively the current is being converted into useful work.

2. **Formula for Power Factor**:
The power factor can be mathematically expressed as:
\[ \text{Power Factor} = \cos \phi \]

3. **Relationship Between R, Z, and φ**:
In an AC circuit, the power factor is also related to the resistance (R) and the impedance (Z) of the circuit. The impedance is the total opposition to current flow in an AC circuit and is given by:
\[ Z = \sqrt{R^2 + X^2} \]
where \(X\) is the reactance of the circuit.

4. **Power Factor in Terms of R and Z**:
The power factor can be expressed as:
\[ \cos \phi = \frac{R}{Z} \]
This means that the power factor is the ratio of the resistance to the impedance.

5. **Conclusion**:
Therefore, the power factor of an AC circuit is given by:
\[ \cos \phi = \frac{R}{Z} \]
This corresponds to option A in the given choices.

### Final Answer:
The power factor of an AC circuit is given by:
\[ \cos \phi = \frac{R}{Z} \]