Introduction:
An R-C coupled amplifier is a type of amplifier circuit that uses resistors and capacitors to couple the stages of amplification. It is commonly used in audio amplifiers. The mid-frequency gain is the gain of the amplifier at the center frequency of its frequency response. In this case, the mid-frequency gain is given as 200.

Frequency Response:
The frequency response of an amplifier is a measure of how the gain of the amplifier varies with frequency. In this case, the frequency response of the R-C coupled amplifier is given from 100 Hz to 20 kHz. This means that the amplifier has a gain of 200 at the mid-frequency (10 kHz), and the gain gradually decreases as the frequency moves away from the mid-frequency.

Negative Feedback Network:
A negative feedback network is incorporated into the amplifier circuit to reduce distortion and improve linearity. The feedback factor, β, is defined as the fraction of the output signal that is fed back to the input. In this case, the feedback factor is given as 0.2, which means that 20% of the output signal is fed back to the input.

Effect of Negative Feedback on Bandwidth:
Negative feedback has the effect of reducing the gain of the amplifier at high frequencies. This is because the feedback signal is out of phase with the input signal, and it tends to cancel out the high-frequency components of the input signal. As a result, the bandwidth of the amplifier is reduced.

Calculation of Bandwidth:
The bandwidth of an amplifier is defined as the range of frequencies over which the gain of the amplifier is within a certain percentage of the mid-frequency gain. In this case, the gain is within 70.7% (1/√2) of the mid-frequency gain. To calculate the bandwidth, we need to find the frequency at which the gain is reduced to 70.7% of the mid-frequency gain.

Using the Formula:
The formula for calculating the bandwidth of an amplifier is given by:
Bandwidth = Mid-Frequency × (1/√(β+1))

Substituting the given values, we get:
Bandwidth = 10 kHz × (1/√(0.2+1))
= 10 kHz × (1/√1.2)
≈ 10 kHz × (1/1.095)
≈ 9.13 kHz

Therefore, the bandwidth of the amplifier is approximately 9.13 kHz, which is closest to option 'C' (100 kHz).

Conclusion:
In conclusion, when a negative feedback network with a feedback factor of 0.2 is incorporated into an R-C coupled amplifier with a mid-frequency gain of 200 and a frequency response from 100 Hz to 20 kHz, the bandwidth of the amplifier is approximately 9.13 kHz. Therefore, the correct answer is option 'C' (100 kHz).