The power factor of a circuit is a measure of how effectively the circuit converts electrical power into useful work. It is defined as the ratio of the real power (P) to the apparent power (S) in the circuit.

The impedance of a circuit is the total opposition to the flow of alternating current (AC) in the circuit. It consists of both resistance (R) and reactance (X). In this case, the impedance of the circuit is given as 3 ohms of resistance and 4 ohms of reactance.

To determine the power factor of the circuit, we need to calculate the real power and the apparent power.

Real Power (P) is the power actually consumed by the circuit in performing useful work. It is given by the formula:
P = I^2 * R
where I is the current flowing through the circuit and R is the resistance.

Apparent Power (S) is the total power supplied to the circuit, including both the real power and any reactive power. It is given by the formula:
S = I^2 * Z
where I is the current flowing through the circuit and Z is the impedance.

To calculate the power factor (PF), we can use the formula:
PF = P / S

Now, let's calculate the real power and the apparent power:

Real Power (P) = I^2 * R = (I^2) * 3
Apparent Power (S) = I^2 * Z = (I^2) * (3 + 4j) (where j represents the imaginary unit)

From the given information, we know that the impedance of the circuit is 3 ohms of resistance and 4 ohms of reactance. Therefore, the power factor (PF) can be calculated as follows:

PF = P / S = (I^2 * 3) / (I^2 * (3 + 4j))

Simplifying the expression, we get:

PF = 3 / (3 + 4j)

To find the power factor, we need to convert the impedance from rectangular form to polar form:

Z = 3 + 4j = 5 * (3/5 + 4/5j)

Now, we can substitute the polar form of the impedance into the power factor equation:

PF = 3 / (5 * (3/5 + 4/5j))

Simplifying further, we get:

PF = 3 / (5 * (3 + 4j) / 5)

PF = 3 / (3 + 4j)

Now, to determine the power factor, we need to find the magnitude of the complex number:

|PF| = |3 / (3 + 4j)|

Using the formula for the magnitude of a complex number, we get:

|PF| = sqrt((3^2) / ((3^2) + (4^2)))

|PF| = sqrt(9 / (9 + 16))

|PF| = sqrt(9 / 25)

|PF| = 3/5

Since the power factor is equal to the magnitude of the complex number, the power factor of the circuit is 0.6. Therefore, the correct answer is option B.