# Step-by-Step Solution Let's solve each task using the given data: - **Load resistance,** \( R = 20\, \Omega \) - **RMS supply voltage,** \( V_{\text{RMS}} = 230\,V \) - **Firing angle,** \( \alpha = 45^\circ \) - **Formula for average output voltage:** \[ V_{dc} = \frac{2V_m}{\pi} \cos \alpha \] - **Peak voltage,** \( V_m = \sqrt{2} \times V_{\text{RMS}} \) --- ## 1. Calculate the **average DC output voltage** ### Step 1: Find the peak voltage \( V_m \) \[ V_m = \sqrt{2} \times 230 = 1.414 \times 230 = 325.27\,V \] ### Step 2: Substitute values into the average output voltage formula \[ V_{dc} = \frac{2 \times 325.27}{\pi} \cos 45^\circ \] ### Step 3: Calculate \( \cos 45^\circ \) \[ \cos 45^\circ = \frac{1}{\sqrt{2}} = .707 \] ### Step 4: Plug in the numbers \[ V_{dc} = \frac{2 \times 325.27}{3.142} \times .707 \] \[ V_{dc} = \frac{650.54}{3.142} \times .707 \] \[ V_{dc} = 207.16 \times .707 \] \[ V_{dc} = 146.48\,V \] --- ## 2. Determine the **load current** \[ I_{dc} = \frac{V_{dc}}{R} = \frac{146.48}{20} = 7.32\,A \] --- ## 3. State whether the SCR conduction is **continuous** - For a **pure resistive load**, the current goes to zero every half-cycle when the supply voltage crosses zero. - **Therefore, the SCR conduction is NOT continuous** for a purely resistive load. --- # **Summary Table** | Quantity | Value | |-------------------|-----------------| | Average DC Voltage| \(146.5 \) V | | Load Current | \(7.32\) A | | SCR Conduction | Not Continuous | --- ## **Final Answers** 1. **Average DC output voltage:** \( \boxed{146.5\ \text{V}} \) 2. **Load current:** \( \boxed{7.32\ \text{A}} \) 3. **SCR conduction is not continuous** for a pure resistive load.