text: # The capacitance Cx of a capacitive type sensor is (1000 x) pF, where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage 10 sin (100π t) V. The other terminal of the sensor is tied to the input of a high input impedance amplifier through a shielded cable, with shield connected to ground. The cable capacitance is 100 pF. The peak of the voltage VA at the input of the amplifier when x = 0.1 (in volts) is
  
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  ## Answer (Detailed Solution Below) 5
  
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  ## Detailed Solution
  
  Capacitance of a capacitive type sensor, Cx = (1000 x) pF
  
  When x = 0.1, Cx = (1000 × 0.1) pF = 100 pF
  
  Cable capacitance = 100 pF
  
  The figure shown below represents the electrical equivalent circuit of the given measurement system.
  
  As the amplifier has high input impedance there will not be any loading effect.
  
  Now, by applying the voltage division rule
  
  $${V_A} = {V_i} \times \frac{{\frac{1}{{j\omega {C_{x}}}}}}{{\frac{1}{{j\omega {C_{cable}}}} + \frac{1}{{j\omega {C_x}}}}}$$
  
  $${V_A} = 10 \times \frac{{{C_{cable}}}}{{{C_x} + {C_{cable}}}}$$
  
  $${V_A} = 10 \times \frac{{100 \times {{10}^{ - 12}}}}{{\left( {100 + 100} \right) \times {{10}^{ - 12}}}} = 5\;V$$
explanation: The document contains a math question related to the capacitance of a capacitive sensor and the voltage at the input of an amplifier. The question is followed by a detailed solution that calculates the peak voltage at the input of the amplifier when the input to the sensor is 0.1. The solution uses the voltage division rule and the given capacitance values to arrive at the answer of 5 volts.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
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  1. Briefly describe the document and mention if it contains a question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: # The capacitance Cx of a capacitive type sensor is (1000 x) pF, where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage 10 sin (100π t) V. The other terminal of the sensor is tied to the input of a high input impedance amplifier through a shielded cable, with shield connected to ground. The cable capacitance is 100 pF. The peak of the voltage VA at the input of the amplifier when x = 0.1 (in volts) is
  
  This question was previously asked in
  GATE IN 2020 Official Paper
  View all GATE IN Papers >
  
  ## Answer (Detailed Solution Below) 5
  
  Free
  GATE IN 2022: Full Mock Test
  0.4 K Users
  65 Questions 100 Marks 180 Mins
  
  ## Detailed Solution
  
  Capacitance of a capacitive type sensor, Cx = (1000 x) pF
  
  When x = 0.1, Cx = (1000 × 0.1) pF = 100 pF
  
  Cable capacitance = 100 pF
  
  The figure shown below represents the electrical equivalent circuit of the given measurement system.
  
  As the amplifier has high input impedance there will not be any loading effect.
  
  Now, by applying the voltage division rule
  
  $${V_A} = {V_i} \times \frac{{\frac{1}{{j\omega {C_{x}}}}}}{{\frac{1}{{j\omega {C_{cable}}}} + \frac{1}{{j\omega {C_x}}}}}$$
  
  $${V_A} = 10 \times \frac{{{C_{cable}}}}{{{C_x} + {C_{cable}}}}$$
  
  $${V_A} = 10 \times \frac{{100 \times {{10}^{ - 12}}}}{{\left( {100 + 100} \right) \times {{10}^{ - 12}}}} = 5\;V$$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question related to the capacitance of a capacitive sensor and the voltage at the input of an amplifier. The question is followed by a detailed solution that calculates the peak voltage at the input of the amplifier when the input to the sensor is 0.1. The solution uses the voltage division rule and the given capacitance values to arrive at the answer of 5 volts.
  
  Label: question-and-answer