To determine the minimum value of the capacitor in a class C commutation circuit used to commutate SCRs, we need to consider the charging current and the time required for the SCRs to turn off.

1. Understanding the Class C Commutation Circuit:
A class C commutation circuit is designed to commutate SCRs (Silicon-Controlled Rectifiers) by providing a reverse voltage across them to turn them off. This circuit consists of an inductor (L), a resistor (R4), and a capacitor (C). The inductor stores energy during the on-state of the SCRs, and when the SCRs turn off, this energy is released through the capacitor, creating a reverse voltage.

2. Determining the Minimum Charging Current:
Each SCR has a minimum charging current of 4 mA to turn it on. This means that the charging current flowing through the inductor should be at least 4 mA to ensure proper turn-on of the SCRs.

3. Calculating the Inductor Charging Current:
The charging current flowing through the inductor can be calculated using Ohm's Law. The voltage across the resistor R2, which is connected in series with the inductor, is given by V = I * R2. Here, V is the voltage across the inductor, I is the charging current, and R2 is the resistance. Given that V = 230 V and R2 = 100 Ω, we can calculate the charging current as follows:
I = V / R2 = 230 V / 100 Ω = 2.3 A

4. Determining the Turn-off Time:
The turn-off time for SCRs is determined by the discharge time of the capacitor through the SCRs' junction capacitance. The time constant (τ) of the circuit can be calculated using the formula τ = R4 * C, where R4 is the resistance and C is the capacitance. The turn-off time (t) is typically considered to be 5 times the time constant (5τ).

5. Calculating the Turn-off Time:
Given that R4 = 20 Ω and the desired turn-off time (t) is not specified, we can assume a desired value for t. Let's assume t = 1 ms. Using the formula τ = R4 * C, we can rearrange the formula to solve for C:
C = τ / R4 = t / (5 * R4) = (1 ms) / (5 * 20 Ω) = 10 μF

6. Determining the Minimum Capacitor Value:
To ensure that the SCRs do not experience a derivative of voltage (dv/dt) when turned on due to reapplied, the minimum value of the capacitor should be such that it provides enough energy to turn off the SCRs without causing excessive voltage changes. A larger capacitor value will result in a slower discharge time, reducing the dv/dt.

In this case, the minimum capacitor value required is 10 μF.

In conclusion, the minimum value of the capacitor in the class C commutation circuit to prevent the SCRs from experiencing a derivative of voltage when turned on due to reapplied is 10 μF. This value is determined based on the minimum charging current of the SCRs and the desired turn-off time.