# Step-by-Step Solution Let’s solve each task step by step: ## 1. Calculate the **average DC output voltage** (\( V_{dc} \)) ### Given: - RMS voltage, \( V_{rms} = 230 \) V - Firing angle, \( \alpha = 45^\circ \) - Load resistance, \( R = 20\, \Omega \) ### Maximum value of supply voltage (\( V_m \)): \[ V_m = \sqrt{2} \times V_{rms} = \sqrt{2} \times 230 = 1.414times 230 = 325.27\, \text} \] ### Average output voltage formula: \[ V_{dc} = \frac{2V_m}{\pi} \cos \alpha \] Plug in the values: \[ V_{dc} = \frac{2 \times 325.27}{\pi} \cos 45^\circ \] \[ \cos 45^\circ = .7071 \] \[ V_{dc} = \frac{650.54}{3.1416} \times .7071 \] \[ V_{dc} = 207.18 \times .7071 \] \[ V_{dc} \approx 146.50\, \text{V} \] --- ## 2. Determine the **load current** (\( I_{dc} \)) \[ I_{dc} = \frac{V_{dc}}{R} \] \[ I_{dc} = \frac{146.50}{20} \] \[ I_{dc} = 7.325\, \text{A} \] --- ## 3. State whether the SCR conduction is **continuous** for this pure resistive load - For a pure resistive load, the load current becomes zero whenever the supply voltage crosses zero. - In this case, since the load is purely resistive, **SCR conduction is NOT continuous**; it is only during the part of the cycle when the SCRs are triggered and the instant supply voltage is positive. --- ## **Final Answers** 1. **Average DC output voltage:** \[ \boxed{146.50\, \text{V}} \] 2. **Load current:** \[ \boxed{7.33\, \text{A}} \] 3. **SCR conduction:** The conduction is **not continuous** for a pure resistive load. --- ### Summary Table | Quantity | Value | |------------------|--------------| | \(V_{dc}\) | 146.50 V | | \(I_{dc}\) | 7.33 A | | SCR conduction | Not continuous|

# Step-by-Step Solution Let’s solve each task step by step: ## 1. Calculate the **average DC output voltage** (\( V_{dc} \)) ### Given: - RMS voltage, \( V_{rms} = 230 \) V - Firing angle, \( \alpha = 45^\circ \) - Load resistance, \( R = 20\, \Omega \) ### Maximum value of supply voltage (\( V_m \)): \[ V_m = \sqrt{2} \times V_{rms} = \sqrt{2} \times 230 = 1.414 \times 230 \approx 325.27\, V \] ### Average output voltage formula: \[ V_{dc} = \frac{2V_m}{\pi} \cos \alpha \] ### Calculation: Substituting the values: \[ V_{dc} = \frac{2 \times 325.27}{\pi} \cos 45^\circ \] \[ \cos 45^\circ = 0.7071 \] \[ V_{dc} = \frac{650.54}{3.1416} \times 0.7071 \approx 207.18 \times 0.7071 \approx 146.50\, V \] --- ## 2. Determine the **load current** (\( I_{dc} \)) Using the formula: \[ I_{dc} = \frac{V_{dc}}{R} \] Substituting the values: \[ I_{dc} = \frac{146.50}{20} \approx 7.325\, A \] --- ## 3. State whether the SCR conduction is **continuous** for this pure resistive load For a pure resistive load: - The load current will drop to zero whenever the supply voltage crosses zero. - Therefore, **SCR conduction is NOT continuous**; it only occurs during the positive half-cycle when the SCRs are conducting. --- ## **Final Answers** 1. **Average DC output voltage:** \[ \boxed{146.50\, V} \] 2. **Load current:** \[ \boxed{7.33\, A} \] 3. **SCR conduction:** The conduction is **not continuous** for a pure resistive load. --- ### Summary Table | Quantity | Value | |------------------|--------------| | \(V_{dc}\) | 146.50 V | | \(I_{dc}\) | 7.33 A | | SCR conduction | Not continuous|