Transformer Utilisation Factor (TUF) of a Half Wave Rectifier

The transformer utilisation factor (TUF) is the ratio of the DC power delivered to the load to the AC rating of the transformer. In a half wave rectifier, TUF is defined as the ratio of the DC output power to the product of the secondary voltage and the secondary current of the transformer.

TUF = DC output power / (V_s x I_s)

Where V_s is the secondary voltage and I_s is the secondary current.

Calculation of TUF for a Half Wave Rectifier

The DC output power of a half wave rectifier is given by:

P_dc = (V_m/π) x I_s x (1 - cos(α))

Where V_m is the maximum value of the secondary voltage and α is the firing angle or the angle between the secondary voltage and the rectified output voltage.

The AC rating of the transformer is given by:

P_ac = V_s x I_s

Therefore, the TUF of a half wave rectifier can be calculated as:

TUF = P_dc / P_ac
= (V_m/π) x (1 - cos(α)) / V_s

For a half wave rectifier, the maximum value of the secondary voltage is equal to the peak value of the input voltage. Therefore,

V_m = V_p

Where V_p is the peak input voltage.

The average value of the output voltage for a half wave rectifier is given by:

V_avg = (V_p / π) x (1 - cos(α))

Therefore, the TUF of a half wave rectifier can be expressed as:

TUF = (1/π) x (1 - cos(α)) / (1/2) x (1 - cos(α/2))

Simplifying this equation, we get:

TUF = 2 / (π x (2 - cos(α)))

For α = 0, TUF = 0

For α = π, TUF = 0.287

Therefore, the correct answer is option C, i.e., 0.287.