Given:
- Two lossy capacitors with equal capacitance values
- Power factor of the first capacitor = 0.01
- Power factor of the second capacitor = 0.02

To find:
- Power factor of the combination

Solution:
When capacitors are connected in parallel, the total capacitance is the sum of individual capacitances.
Let the capacitance of each capacitor be C.

Power factor:
Power factor (PF) is the cosine of the angle between the voltage and current waveforms in an AC circuit. It is a measure of how effectively the circuit converts electrical power into useful work.

Key points:
- A capacitor has a leading power factor, meaning the current leads the voltage by some angle.
- The power factor of a capacitor can be calculated using the formula: PF = cos(θ), where θ is the phase angle between the voltage and current waveforms.
- The power factor can also be calculated as the ratio of the real power (P) to the apparent power (S), i.e., PF = P/S.

Calculation:
Power factor of the first capacitor:
Given power factor = 0.01
Let the angle between the voltage and current waveforms of the first capacitor be θ1.

Using the formula PF = cos(θ), we have:
0.01 = cos(θ1)

Taking the inverse cosine of both sides, we get:
θ1 = arccos(0.01)

Similarly, for the second capacitor:
Given power factor = 0.02
Let the angle between the voltage and current waveforms of the second capacitor be θ2.

Using the formula PF = cos(θ), we have:
0.02 = cos(θ2)

Taking the inverse cosine of both sides, we get:
θ2 = arccos(0.02)

Power factor of the combination:
When capacitors are connected in parallel, the total capacitance is the sum of individual capacitances.
Let the total capacitance be C_total = 2C (since both capacitors have equal capacitance).

The total current supplied by the sinusoidal voltage source can be calculated as the sum of the individual currents through each capacitor.
Let the current through the first capacitor be I1 and the current through the second capacitor be I2.

The total current I_total = I1 + I2

The power factor of the combination is given by the ratio of the total real power to the total apparent power:
PF_total = (P_total) / (S_total)

Since power factor is a measure of how effectively the circuit converts electrical power into useful work, the total real power (P_total) can be calculated as the sum of the real powers of each capacitor.

The total apparent power (S_total) can be calculated as the sum of the apparent powers of each capacitor.

To find the power factor of the combination, we need to calculate the total real power and the total apparent power.

Total real power:
The real power (P) of a capacitor can be calculated using the formula: P = VIcos(θ), where V is the voltage across the capacitor and θ is the phase angle between the voltage and current waveforms.

The voltage across each capacitor is the same, equal to the supply voltage.

The real power of