Question

For the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is \( I_{\text{dc}} = 15 \, \text{A} \) and is ripple free. The thyristors are fired with a delay angle of 45°. The amplitude of the fundamental component of the source current, in amperes, is ________. (round off to two decimal places)

Hint:

For AC-DC rectifiers, the amplitude of the fundamental component of the source current can be calculated using \( I_{\text{fundamental}} = \frac{I_{\text{dc}}}{\cos(\alpha)} \), where \( \alpha \) is the delay angle.

Answer 1

Correct Answer: 17.3

For an ideal AC-DC rectifier with a delay angle \( \alpha \), the amplitude of the fundamental component of the source current \( I_{\text{fundamental}} \) is related to the DC current \( I_{\text{dc}} \) by the following formula: \[ I_{\text{fundamental}} = \frac{I_{\text{dc}}}{\cos(\alpha)}. \] Given:
- \( I_{\text{dc}} = 15 \, \text{A} \),
- \( \alpha = 45^\circ \),
Substituting the values: \[ I_{\text{fundamental}} = \frac{15}{\cos(45^\circ)} = \frac{15}{\frac{\sqrt{2}}{2}} = 15 \times \frac{\sqrt{2}}{2} = 15 \times 0.707 \approx 10.61 \, \text{A}. \] Thus, the amplitude of the fundamental component of the source current is approximately \( \boxed{10.61} \) A.