Topic: Power Electronics
In a single-phase full-wave controlled rectifier using SCRs with a resistive load, the firing angle is set to $\alpha=60^{\circ}.$ Which of the following statements is TRUE regarding the average output voltage (V_avg)? Assume ideal conditions. $V_{m}=$ the peak input voltage
- A. $V_{\_}avg=(V_{m}/\pi)(1+\cos(60^{\circ}))$
- B. $V_{\_}avg=(2V_{m}/\pi)(1-\cos(60^{\circ}))$
- C. $V_{\_}avg=(2V_{m}/\pi)(1+\cos(60^{\circ}))$
- D. $V_{\_}avg=V_{m}\cos(60^{\circ})$
Answer: A. $V_{\_}avg=(V_{m}/\pi)(1+\cos(60^{\circ}))$
Explanation: For a single-phase full-wave fully controlled rectifier with a purely resistive load, the average output voltage is calculated by integrating the output waveform over one half-cycle: $V_{avg} = \frac{1}{\pi} \int_{\alpha}^{\pi} V_m \sin(\omega t) d(\omega t)$. Evaluating the integral gives $V_{avg} = \frac{V_m}{\pi} [-\cos(\omega t)]_{\alpha}^{\pi} = \frac{V_m}{\pi} (1 + \cos\alpha)$. Substituting $\alpha = 60^{\circ}$ yields $V_{avg} = (V_m/\pi)(1+\cos(60^{\circ}))$.