Given Information:
R1 = 8 ohms
C1 = 800 uF
C2 = 250 uF
R2 = 3.5 ohms
V (input voltage) = ?
I (current) = 10 A
Frequency = 60 Hz

Calculating Impedance:
First, we need to calculate the impedance of the circuit. Impedance (Z) in a series circuit is given by the formula:

Z = √(R^2 + (Xc1 - Xc2)^2)

Where R is the resistance and Xc1 and Xc2 are the reactances of C1 and C2, respectively.

Reactance (Xc) for a capacitor is given by the formula:

Xc = 1 / (2πfC)

Where f is the frequency and C is the capacitance.

For C1:
Xc1 = 1 / (2πfC1) = 1 / (2π * 60 * 800 * 10^(-6)) ≈ 33.33 ohms

For C2:
Xc2 = 1 / (2πfC2) = 1 / (2π * 60 * 250 * 10^(-6)) ≈ 53.33 ohms

Plugging in the values, we get:
Z = √(8^2 + (33.33 - 53.33)^2) ≈ √(64 + 400) ≈ √464 ≈ 21.54 ohms

Calculating Power Factor:
Power factor (PF) is the ratio of the real power (P) to the apparent power (S) in a circuit. It is given by the formula:

PF = P / S

Real power (P) in a circuit is given by the formula:

P = VI * cos(θ)

Where V is the voltage and I is the current.

Apparent power (S) in a circuit is given by the formula:

S = VI

To calculate the power factor, we need to find the voltage.

Using Ohm's Law:
V = I * Z = 10 * 21.54 ≈ 215.4 volts

Now, plugging in the values, we get:
P = 215.4 * 10 * cos(θ)
S = 215.4 * 10

PF = P / S = (215.4 * 10 * cos(θ)) / (215.4 * 10)

Simplifying:
PF = cos(θ)

Therefore, the power factor of the circuit is equal to the cosine of the phase angle (θ).

Conclusion:
The power factor of the circuit can be calculated using the cosine of the phase angle (θ), which is equal to the impedance (Z) divided by the magnitude of the impedance (|Z|). In this case, the power factor can be determined by calculating the impedance and finding the cosine of the phase angle. The power factor is an important parameter in AC circuits as it indicates the efficiency of power transfer and the level of reactive power in the circuit.