Firing-angle delay is a term used in power electronics to describe the delay between the application of a control signal and the firing of a thyristor or other solid-state switching device. It is an important parameter in controlling the output power of a converter or inverter circuit.

The firing-angle delay is directly proportional to the control signal voltage. This means that as the control signal voltage increases, the firing-angle delay also increases.

To understand why this is the case, let's consider the operation of a typical thyristor-based converter circuit. The thyristor is a four-layer, three-terminal semiconductor device that acts as a switch. It can be turned on by applying a positive gate voltage with respect to the cathode.

- **Control signal voltage and firing-angle delay:**
The control signal voltage is the voltage applied to the gate terminal of the thyristor to turn it on. Increasing the control signal voltage increases the gate current, which reduces the firing-angle delay. This is because a higher gate current allows the thyristor to turn on more quickly, reducing the delay between the application of the control signal and the firing of the thyristor.

- **Inversely proportional to the synchronizing transformer voltage:**
The synchronizing transformer voltage refers to the voltage level at which the transformer operates. It is not directly related to the firing-angle delay. Therefore, option 'A' is incorrect.

- **Inversely proportional to the control signal voltage:**
The firing-angle delay is directly proportional to the control signal voltage, not inversely proportional to it. Therefore, option 'B' is incorrect.

- **Directly proportional to the synchronizing transformer voltage:**
The firing-angle delay is not directly related to the synchronizing transformer voltage. Therefore, option 'C' is incorrect.

In conclusion, the firing-angle delay is directly proportional to the control signal voltage. Increasing the control signal voltage reduces the delay between the application of the control signal and the firing of the thyristor. This relationship is important in power electronics applications where precise control of the output power is required.