{
  "title": "sri answer 3",
  "taskId": "9e2e2a8d-a359-4fae-860d-d4724b60c61d",
  "type": "SOLUTION",
  "timestamp": 1792253532456,
  "doc": {
    "type": "doc",
    "content": [
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "Given Data :"
          }
        ]
      },
      {
        "type": "bulletList",
        "content": [
          {
            "type": "listItem",
            "content": [
              {
                "type": "paragraph",
                "attrs": {
                  "textAlign": "left"
                },
                "content": [
                  {
                    "type": "text",
                    "text": "Input Mains Voltage : "
                  },
                  {
                    "type": "inlineMath",
                    "attrs": {
                      "mathType": "asciimath"
                    },
                    "content": [
                      {
                        "type": "text",
                        "text": "V_(i n)=230V(rms)"
                      }
                    ]
                  }
                ]
              }
            ]
          },
          {
            "type": "listItem",
            "content": [
              {
                "type": "paragraph",
                "attrs": {
                  "textAlign": "left"
                },
                "content": [
                  {
                    "type": "text",
                    "text": "Series protection resistance : "
                  },
                  {
                    "type": "inlineMath",
                    "attrs": {
                      "mathType": "asciimath"
                    },
                    "content": [
                      {
                        "type": "text",
                        "text": "R_s=200Omega"
                      }
                    ]
                  }
                ]
              }
            ]
          },
          {
            "type": "listItem",
            "content": [
              {
                "type": "paragraph",
                "attrs": {
                  "textAlign": "left"
                },
                "content": [
                  {
                    "type": "text",
                    "text": "Line current drawn from mains :"
                  },
                  {
                    "type": "inlineMath",
                    "attrs": {
                      "mathType": "asciimath"
                    },
                    "content": [
                      {
                        "type": "text",
                        "text": "I_(i n)=0.5A(rms)"
                      }
                    ]
                  }
                ]
              }
            ]
          },
          {
            "type": "listItem",
            "content": [
              {
                "type": "paragraph",
                "attrs": {
                  "textAlign": "left"
                },
                "content": [
                  {
                    "type": "text",
                    "text": "Load resistance :"
                  },
                  {
                    "type": "inlineMath",
                    "attrs": {
                      "mathType": "asciimath"
                    },
                    "content": [
                      {
                        "type": "text",
                        "text": "R_L=500Omega"
                      }
                    ]
                  }
                ]
              }
            ]
          },
          {
            "type": "listItem",
            "content": [
              {
                "type": "paragraph",
                "attrs": {
                  "textAlign": "left"
                },
                "content": [
                  {
                    "type": "text",
                    "text": "Peak-to-peak output ripple voltage :"
                  },
                  {
                    "type": "inlineMath",
                    "attrs": {
                      "mathType": "asciimath"
                    },
                    "content": [
                      {
                        "type": "text",
                        "text": "V_r=20V"
                      }
                    ]
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "marks": [
              {
                "type": "bold"
              }
            ],
            "text": "Step "
          },
          {
            "type": "text",
            "text": "1: Find the total AC input Power "
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        }
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "Since the system operates at unity power factor (pf=1):"
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "P_(i n) = V_(i n)*I_(i n)*pf"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 230*0.5*1"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 115W"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        }
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "marks": [
              {
                "type": "bold"
              }
            ],
            "text": "Step "
          },
          {
            "type": "text",
            "text": "2: Power Dissipated in the Series Resistance "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "R_s"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "The true power loss across the series resistance uses the RMS line current :"
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "P_(Rs) = I_(i n)^2*R_s"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
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            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 0.5^2*200"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 50W"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        }
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "Step 3: Peak Voltages and Waveform Geometry "
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        }
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "The RMS voltage entering the rectifier stage after the series resistor drop is :"
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
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            "attrs": {
              "mathType": "asciimath"
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            "content": [
              {
                "type": "text",
                "text": "V_(rect(rms) = V_(i n)-(I_(i n)*R_s)"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 230-(0.5*200)"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 130V"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "The maximum peak voltage ("
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "V_(m1)"
              }
            ]
          },
          {
            "type": "text",
            "text": ") is :"
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
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            "attrs": {
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            },
            "content": [
              {
                "type": "text",
                "text": "V_(m1) = sqrt2*V_(rect(rms)"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= sqrt2*130"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
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            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 183.8478V"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        }
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "The minimum v=Trough voltage "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "(V_(m2))"
              }
            ]
          },
          {
            "type": "text",
            "text": " considering the 20V peak-to-peak ripple voltage "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "(V_r)"
              }
            ]
          },
          {
            "type": "text",
            "text": " is :"
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "V_(m2) = V_(m1)-V_r"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 183.8478-20"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
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            "content": [
              {
                "type": "text",
                "text": "= 163.8478V"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        }
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "marks": [
              {
                "type": "bold"
              }
            ],
            "text": "Step 4: "
          },
          {
            "type": "text",
            "text": "Total DC Output Voltage Across Load "
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        }
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "The average DC voltage "
          },
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            "attrs": {
              "mathType": "asciimath"
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            "content": [
              {
                "type": "text",
                "text": "(V_(out))"
              }
            ]
          },
          {
            "type": "text",
            "text": " delivered to the load resistor is the mean value of the ripple waveform extremes:"
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
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            "attrs": {
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            "content": [
              {
                "type": "text",
                "text": "V_(out) = (V_(m1)+V_(m2))/2"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
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            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= (183.8478+163.8478)/2"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
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            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 173.8478V"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "marks": [
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                "type": "bold"
              }
            ],
            "text": "Step 5: "
          },
          {
            "type": "text",
            "text": "Output DC Load Power "
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "The power delivered to the resistive load "
          },
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "R_L"
              }
            ]
          },
          {
            "type": "text",
            "text": " is :"
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
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        "content": [
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            "type": "inlineMath",
            "attrs": {
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            },
            "content": [
              {
                "type": "text",
                "text": "P_(out) = V_(out)^2/R_L"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
            },
            "content": [
              {
                "type": "text",
                "text": "= 173.8478^2/500"
              }
            ]
          }
        ]
      },
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        "type": "paragraph",
        "attrs": {
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        },
        "content": [
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            "attrs": {
              "mathType": "asciimath"
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            "content": [
              {
                "type": "text",
                "text": "= 60.4461W"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
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            "text": "Step 6:"
          },
          {
            "type": "text",
            "text": " Operating Efficiency "
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
          "textAlign": "left"
        },
        "content": [
          {
            "type": "text",
            "text": "The total efficiency "
          },
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            "attrs": {
              "mathType": "asciimath"
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            "content": [
              {
                "type": "text",
                "text": "(eta)"
              }
            ]
          },
          {
            "type": "text",
            "text": " of the rectifier circuit is :"
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
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        "content": [
          {
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            "attrs": {
              "mathType": "asciimath"
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            "content": [
              {
                "type": "text",
                "text": "eta = P_(out)/P_(i n)*100%"
              }
            ]
          }
        ]
      },
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        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
          {
            "type": "inlineMath",
            "attrs": {
              "mathType": "asciimath"
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            "content": [
              {
                "type": "text",
                "text": "= 60.4461/115*100%"
              }
            ]
          }
        ]
      },
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        "type": "paragraph",
        "attrs": {
          "textAlign": "center"
        },
        "content": [
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            "attrs": {
              "mathType": "asciimath"
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            "content": [
              {
                "type": "text",
                "text": "= 52.56%"
              }
            ]
          }
        ]
      },
      {
        "type": "paragraph",
        "attrs": {
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        }
      },
      {
        "type": "paragraph",
        "attrs": {
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        "content": [
          {
            "type": "text",
            "text": "The final answer is "
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            "content": [
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                "type": "text",
                "text": "eta=52.56%"
              }
            ]
          },
          {
            "type": "text",
            "text": "."
          }
        ]
      }
    ]
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                          "text": "Input Mains Voltage : "
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                              "text": "V_(i n)=230V(rms)"
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                          "text": "Series protection resistance : "
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                              "text": "R_s=200Omega"
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                          "text": "Line current drawn from mains :"
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                              "text": "I_(i n)=0.5A(rms)"
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                          "text": "Load resistance :"
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                              "text": "R_L=500Omega"
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