Final answer:
The common-mode choke will have a negligible effect on signal transmission above approximately 3236 Hz.
Step-by-step explanation:
The common-mode choke will start having a negligible effect on the signal transmission when its impedance becomes much larger than the impedance of the transmission line. In this case, the transmission line has a low impedance of 1Ω resistive component and the load has an impedance of 900Ω. Above what frequency the choke will have a negligible effect on signal transmission is when its reactance is much larger than 900Ω. The reactance of the choke in series with the load will be at its maximum when its inductive reactance is much larger than its resistance. Since each winding of the choke has an inductance of 0.044H and resistance of 4Ω, the choke's inductive reactance will be much larger than its resistance at frequencies above a certain cutoff frequency.
The inductive reactance (XL) can be calculated using the formula XL = 2πfL, where f is the frequency and L is the inductance. Equating the XL to the resistance of the load, we can find the cutoff frequency.
So, at the cutoff frequency, XL = R = 900Ω. Rearranging the formula, we get f = R / (2πL). Substituting the values, we get f = 900 / (2π * 0.044) ≈ 3236 Hz.
Therefore, above approximately 3236 Hz, the common-mode choke will have a negligible effect on the signal transmission.