The duty cycle of a chopper is defined as the ratio of the time the output is in the active state (on time) to the total time of one cycle (on time plus off time). It is usually expressed as a percentage. Mathematically, it can be represented as:

[ text{Duty Cycle} (%) = left( frac{T_{on}}{T_{on} + T_{off}} right) times 100 ]

Where:

– ( T_{on} ) is the time the chopper is turned on,

– ( T_{off} ) is the time the chopper is turned off.

In chopper circuits, the duty cycle affects the output voltage and power delivered to the load. A higher duty cycle means the chopper is on for a longer time, resulting in higher output voltage and power.

To calculate the average and RMS currents for an SCR conducting in a resistive circuit with a rectangular wave and a conduction angle of 90°, we can use the following formulas.

1. Average Current (I_avg) for a rectangular waveform when the conduction angle is 90°:

[

I_{avg} = frac{I_{max}}{pi}

]

Where ( I_{max} ) is the maximum (RMS) on-state current, which is 35 A.

[

I_{avg} = frac{35}{pi} approx 11.14 , A

]

2. RMS Current (I_rms) for the same waveform:

[

I_{rms} = I_{max} times sqrt{frac{theta}{360}} = I_{max} times sqrt{frac{90}{360}} = I_{max} times sqrt{frac{1}{4}} = frac{I_{max}}{2}

]

So the RMS current would be:

[

I_{rms} = frac{35}{2} = 17.5 , A

]

Based on this, the average and RMS currents are approximately:

– Average Current (I_avg): 11.14 A

– RMS Current (I_rms): 17.

To calculate the average on-state current rating (ITAV) for an SCR, using the provided values:

We have:

– Average current (Iavg) = I/4

– RMS current (Irms) = I/2

– Maximum RMS on-state current (Irms_max) = 35 A

1. Since we have the IRMS expression:

[

I = 2 times Irms = 2 times (I/2) = I implies Irms = I/2 quad text{(already given)}

]

2. Substitute the given ( Irms ):

[

I/2 = 35 A implies I = 70 A

]

3. Calculate the average current:

[

Iavg = I/4 = 70 A / 4 = 17.5 A

]

Thus, the average on-state current rating (ITAV) is 17.5 A.

Final answer:

ITAV = 17.5 A