Introduction:
In this scenario, we have a 10 μF capacitor being fed from an AC voltage source that contains a fundamental frequency and a third harmonic of strength one-third of the fundamental. We need to determine the third harmonic current flowing through the capacitor expressed as a percentage of the fundamental under steady-state conditions.

Understanding the problem:
To solve this problem, we need to understand the behavior of capacitors in AC circuits and how they respond to different frequencies. Capacitors act as a short circuit to high frequencies and an open circuit to low frequencies. Therefore, the impedance of a capacitor is inversely proportional to the frequency of the AC signal.

Analysis:
To find the third harmonic current flowing through the capacitor, we need to analyze the impedance of the capacitor at the third harmonic frequency and compare it to the impedance at the fundamental frequency.

Impedance at the fundamental frequency:
The impedance (Z) of a capacitor is given by the formula:
Z = 1 / (2πfC)
where f is the frequency and C is the capacitance.

At the fundamental frequency, the impedance of the capacitor can be calculated as:
Z_fundamental = 1 / (2πf_c * C)
where f_c is the frequency of the fundamental.

Impedance at the third harmonic frequency:
The third harmonic frequency (f_3rd) is three times the frequency of the fundamental (f_c).
Therefore, the impedance of the capacitor at the third harmonic frequency can be calculated as:
Z_3rd = 1 / (2πf_3rd * C) = 1 / (2π * 3f_c * C) = 1 / (6πf_c * C)

Calculating the third harmonic current:
The third harmonic current (I_3rd) can be calculated using Ohm's Law:
I_3rd = V / Z_3rd
where V is the voltage across the capacitor.

To find the percentage of the third harmonic current with respect to the fundamental, we can express it as a ratio of I_3rd to the fundamental current (I_fundamental) and multiply by 100.
Percentage of third harmonic current = (I_3rd / I_fundamental) * 100

Substituting the values:
Given that the strength of the third harmonic is one-third of the fundamental, we can assume that the voltage across the capacitor is the same for both frequencies.
Therefore, V_3rd = V_fundamental

By substituting the values of Z_3rd and Z_fundamental, we can calculate the third harmonic current and express it as a percentage of the fundamental current.

Conclusion:
In this problem, we analyzed the impedance of a capacitor at the fundamental and third harmonic frequencies to calculate the third harmonic current flowing through the capacitor. By comparing the impedance at these frequencies and using Ohm's Law, we determined the third harmonic current as a percentage of the fundamental current. This analysis helps us understand the behavior of capacitors in AC circuits and their response to different frequencies.