# 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

$${V_A} = {V_i} \times \frac{{\frac{1}{{j\omega {C_{x}}}}}}{{\frac{1}{{j\omega {C_{cable}}}} + \frac{1}{{j\omega {C_x}}}}}$$

$${V_A} = 10 \times \frac{{{C_{cable}}}}{{{C_x} + {C_{cable}}}}$$

$${V_A} = 10 \times \frac{{100 \times {{10}^{ - 12}}}}{{\left( {100 + 100} \right) \times {{10}^{ - 12}}}} = 5\;V$$
The text passage contains a mathematical question related to calculating the peak voltage at the input of an amplifier in a capacitive sensor circuit. The answer to this question is provided at the end of the passage.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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

$${V_A} = {V_i} \times \frac{{\frac{1}{{j\omega {C_{x}}}}}}{{\frac{1}{{j\omega {C_{cable}}}} + \frac{1}{{j\omega {C_x}}}}}$$

$${V_A} = 10 \times \frac{{{C_{cable}}}}{{{C_x} + {C_{cable}}}}$$

$${V_A} = 10 \times \frac{{100 \times {{10}^{ - 12}}}}{{\left( {100 + 100} \right) \times {{10}^{ - 12}}}} = 5\;V$$
user
The text passage contains a mathematical question related to calculating the peak voltage at the input of an amplifier in a capacitive sensor circuit. The answer to this question is provided at the end of the passage.

TYPE: SINGLE_QUESTION_WITH_ANSWER