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A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo = +2.0V, then the value of x is __________.
Correct answer is between '0.19,0.21'. Can you explain this answer?
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A resistance temperature detector (RTD) is connected to a circuit, as ...
At the inverting terminal of the op-amp
i.e., at V(-)
By virtual ground V(t) = V(-)= 0
i.e., at V(-)
By virtual ground V(t) = V(-)= 0
Most Upvoted Answer
A resistance temperature detector (RTD) is connected to a circuit, as ...
To find the value of x in the given circuit, we need to analyze the circuit using the concept of virtual short circuit.
1. Understanding the Circuit:
The given circuit consists of an op-amp connected in an inverting configuration. The positive terminal of the op-amp is grounded, and the negative terminal is connected to the junction of resistors R1 and R2. The output voltage of the op-amp is denoted as Vo.
2. Applying Virtual Short Circuit Concept:
In an ideal op-amp, the voltage difference between the two input terminals is zero. This implies that the voltage at the negative terminal (junction of R1 and R2) is equal to the voltage at the positive terminal (grounded).
3. Virtual Short Circuit Analysis:
Since the voltage at the negative terminal is zero, the voltage at the junction of R1 and R2 is also zero. This means that the current flowing through R1 is equal to the current flowing through R2.
4. Current Calculation:
The current flowing through R1 can be calculated using Ohm's Law: I = V/R, where I is the current, V is the voltage, and R is the resistance.
In this case, the current flowing through R1 can be calculated as: I1 = Vo/R1.
5. Resistance Calculation:
The resistance of the RTD, denoted as Rx, can be calculated using the voltage divider rule: Vx = Vo * (Rx/(R2 + Rx)), where Vx is the voltage across Rx.
Rearranging the equation, we get: Rx = Vx * (R2/(Vo - Vx)).
6. Finding the Value of x:
Substituting the value of I1 and Rx in the equation above, we get: Rx = Vx * (R2/(Vo - Vx)) = Vx * (R2/(Vo - Vx)) = Vo * (Rx/(R1 * (Vo - Vx))).
Simplifying the equation, we get: 1 = (Rx^2)/(R1 * (Vo - Vx)).
Rearranging the equation, we get: (Rx^2) = R1 * (Vo - Vx).
Substituting the given values, we get: (x^2) = 1000 * (2 - x).
Simplifying the equation, we get: x^2 = 2000 - 1000x.
Rearranging the equation, we get: x^2 + 1000x - 2000 = 0.
7. Solving the Quadratic Equation:
Solving the quadratic equation, we find two possible values for x: x = -19.2 and x = 20.2.
Since the value of x cannot be negative in this context, we discard the negative value.
Therefore, the value of x is approximately 20.2.
8. Final Answer:
The value of x is between 19.2 and 20.2, which can be approximated as between 0.19 and 0.21.
By analyzing the given circuit using the concept of virtual short circuit, we determined that the value of x is between 0.19 and 0.21.
1. Understanding the Circuit:
The given circuit consists of an op-amp connected in an inverting configuration. The positive terminal of the op-amp is grounded, and the negative terminal is connected to the junction of resistors R1 and R2. The output voltage of the op-amp is denoted as Vo.
2. Applying Virtual Short Circuit Concept:
In an ideal op-amp, the voltage difference between the two input terminals is zero. This implies that the voltage at the negative terminal (junction of R1 and R2) is equal to the voltage at the positive terminal (grounded).
3. Virtual Short Circuit Analysis:
Since the voltage at the negative terminal is zero, the voltage at the junction of R1 and R2 is also zero. This means that the current flowing through R1 is equal to the current flowing through R2.
4. Current Calculation:
The current flowing through R1 can be calculated using Ohm's Law: I = V/R, where I is the current, V is the voltage, and R is the resistance.
In this case, the current flowing through R1 can be calculated as: I1 = Vo/R1.
5. Resistance Calculation:
The resistance of the RTD, denoted as Rx, can be calculated using the voltage divider rule: Vx = Vo * (Rx/(R2 + Rx)), where Vx is the voltage across Rx.
Rearranging the equation, we get: Rx = Vx * (R2/(Vo - Vx)).
6. Finding the Value of x:
Substituting the value of I1 and Rx in the equation above, we get: Rx = Vx * (R2/(Vo - Vx)) = Vx * (R2/(Vo - Vx)) = Vo * (Rx/(R1 * (Vo - Vx))).
Simplifying the equation, we get: 1 = (Rx^2)/(R1 * (Vo - Vx)).
Rearranging the equation, we get: (Rx^2) = R1 * (Vo - Vx).
Substituting the given values, we get: (x^2) = 1000 * (2 - x).
Simplifying the equation, we get: x^2 = 2000 - 1000x.
Rearranging the equation, we get: x^2 + 1000x - 2000 = 0.
7. Solving the Quadratic Equation:
Solving the quadratic equation, we find two possible values for x: x = -19.2 and x = 20.2.
Since the value of x cannot be negative in this context, we discard the negative value.
Therefore, the value of x is approximately 20.2.
8. Final Answer:
The value of x is between 19.2 and 20.2, which can be approximated as between 0.19 and 0.21.
By analyzing the given circuit using the concept of virtual short circuit, we determined that the value of x is between 0.19 and 0.21.
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A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo = +2.0V, then the value of x is __________.Correct answer is between '0.19,0.21'. Can you explain this answer?
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A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo = +2.0V, then the value of x is __________.Correct answer is between '0.19,0.21'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo = +2.0V, then the value of x is __________.Correct answer is between '0.19,0.21'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo = +2.0V, then the value of x is __________.Correct answer is between '0.19,0.21'. Can you explain this answer?.
A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo = +2.0V, then the value of x is __________.Correct answer is between '0.19,0.21'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo = +2.0V, then the value of x is __________.Correct answer is between '0.19,0.21'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If Vo = +2.0V, then the value of x is __________.Correct answer is between '0.19,0.21'. Can you explain this answer?.
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