In a load-commutated chopper the commutating capacitor is charged and then reversed by the load current itself, and the time that takes is what limits how fast the chopper can be switched.

Step 1 — the reversal time. A capacitor charged to +V must be driven to −V by a constant load current I. Since \(I=C\dfrac{dv}{dt}\) with a total swing of 2V,

\(t_{c}=\dfrac{C\left(2V\right)}{I}=\dfrac{2CV}{I}\)

Step 2 — tie it to the maximum frequency. The commutation must fit inside one chopping period, so at the highest frequency the period is entirely taken by it:

\(T_{min}=\dfrac{1}{f_{max}}=\dfrac{2CV}{I}\qquad\Rightarrow\qquad C=\dfrac{I}{2\,V\,f_{max}}\)

Step 3 — substitute.

\(C=\dfrac{100}{2\times100\times5000}=\dfrac{100}{10^{6}}=100\ \mu\text{F}\)

which is option 1.

Check the consistency : with C = 100 μF, \(\dfrac{CV}{I}=\dfrac{10^{-4}\times100}{100}=100\ \mu\text{s}\), so the full reversal takes 200 μs — exactly one period at 5 kHz. The answer is flagged for confirmation because different textbooks define the commutation interval as \(CV/I\) or \(2CV/I\), and the offered options include both 50 μF and 200 μF, which are what those alternative conventions would give.

Why forced commutation is needed at all. A thyristor conducting from a DC supply has no natural current zero to turn it off, so an auxiliary circuit must drive its current below the holding value and hold reverse voltage across it for at least the device's turn-off time t_q. The capacitor is the energy store that does this, which is why its value scales with the current to be commutated and inversely with the available voltage.

The design tension the formula exposes : a larger C commutates a larger current safely but lengthens the dead time and so lowers the maximum chopping frequency — and a lower frequency means larger filter components and coarser control of the motor. Faster switching devices (GTOs, IGBTs) removed this constraint entirely by turning off from their own gate, which is why load-commutated choppers are now historical.

Hence, the commutating capacitance is 100 μF.