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Questions and Answers
What effect do leadwire resistances have in a strain gage bridge configuration?
What effect do leadwire resistances have in a strain gage bridge configuration?
How does a three-wire connection assist in strain gage bridges?
How does a three-wire connection assist in strain gage bridges?
What is the primary role of a capacitor in a circuit?
What is the primary role of a capacitor in a circuit?
According to Ohm's law, what does the equation V = IR represent?
According to Ohm's law, what does the equation V = IR represent?
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What determines the resistance of a wire according to the formula R = ρL/A?
What determines the resistance of a wire according to the formula R = ρL/A?
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What is the formula for calculating the equivalent resistance in a series circuit?
What is the formula for calculating the equivalent resistance in a series circuit?
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What does Faraday's law of induction relate to in an inductor?
What does Faraday's law of induction relate to in an inductor?
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Which law states that the sum of the currents flowing into a closed surface or node is zero?
Which law states that the sum of the currents flowing into a closed surface or node is zero?
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What is the general form of the voltage divider equation for a resistor Ri?
What is the general form of the voltage divider equation for a resistor Ri?
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Which of the following statements best describes Kirchhoff's voltage law?
Which of the following statements best describes Kirchhoff's voltage law?
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What is the typical range of capacitance for capacitors?
What is the typical range of capacitance for capacitors?
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How do you find the equivalent capacitance of capacitors in series?
How do you find the equivalent capacitance of capacitors in series?
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In a parallel circuit, how is the equivalent resistance calculated?
In a parallel circuit, how is the equivalent resistance calculated?
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What is the condition to maximize power transmitted to the load in an impedance matching scenario?
What is the condition to maximize power transmitted to the load in an impedance matching scenario?
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Which equation represents the power transmitted to the load in an impedance matching scenario?
Which equation represents the power transmitted to the load in an impedance matching scenario?
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What describes a current divider in a parallel circuit?
What describes a current divider in a parallel circuit?
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What is the main function of a Wheatstone bridge?
What is the main function of a Wheatstone bridge?
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In a balanced Wheatstone bridge, what does the galvanometer indicate?
In a balanced Wheatstone bridge, what does the galvanometer indicate?
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Which method is used for measuring dynamic signals with a Wheatstone bridge?
Which method is used for measuring dynamic signals with a Wheatstone bridge?
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What characteristic is assumed for the resistances in the Wheatstone bridge for simplification?
What characteristic is assumed for the resistances in the Wheatstone bridge for simplification?
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What happens to the effective bridge resistance when the Wheatstone bridge is slightly unbalanced?
What happens to the effective bridge resistance when the Wheatstone bridge is slightly unbalanced?
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Which variable represents the voltage impressed on the bridge in an unbalanced condition?
Which variable represents the voltage impressed on the bridge in an unbalanced condition?
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In voltage divider relations, what does VA represent?
In voltage divider relations, what does VA represent?
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If the resistance R1 changes by an amount ΔR1, what formula describes the change in electromotive force (Eg)?
If the resistance R1 changes by an amount ΔR1, what formula describes the change in electromotive force (Eg)?
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What effect do long leadwires have in a Wheatstone bridge setup?
What effect do long leadwires have in a Wheatstone bridge setup?
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Which variable is typically used to represent the effective resistance as presented to the galvanometer in an unbalanced Wheatstone bridge?
Which variable is typically used to represent the effective resistance as presented to the galvanometer in an unbalanced Wheatstone bridge?
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Flashcards
Wheatstone Bridge
Wheatstone Bridge
A circuit used to measure unknown resistance by balancing the bridge with known resistances. It consists of four resistors connected in a diamond shape.
Ratio Arms
Ratio Arms
The two resistors in a Wheatstone bridge that are used to set the ratio for measuring the unknown resistance. They are typically fixed resistances.
Balanced Bridge
Balanced Bridge
A Wheatstone bridge where the voltage difference between two specific points is zero. This signifies that the unknown resistance is balanced by the known resistances.
Transducer
Transducer
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Deflection Bridge
Deflection Bridge
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Effective Resistance
Effective Resistance
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How does a Wheatstone Bridge measure resistance?
How does a Wheatstone Bridge measure resistance?
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What is the difference between a balanced and unbalanced bridge?
What is the difference between a balanced and unbalanced bridge?
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Why are leadwire resistances important in Wheatstone Bridge measurements?
Why are leadwire resistances important in Wheatstone Bridge measurements?
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What is the application of the Wheatstone Bridge in dynamic signal measurement?
What is the application of the Wheatstone Bridge in dynamic signal measurement?
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Leadwire Resistance Effects
Leadwire Resistance Effects
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Three-Wire Connection Advantage
Three-Wire Connection Advantage
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Resistance Formula
Resistance Formula
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Ohm's Law
Ohm's Law
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Capacitor Function
Capacitor Function
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Capacitor Voltage-Current Relationship
Capacitor Voltage-Current Relationship
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Inductor Function
Inductor Function
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Inductor Voltage-Current Relationship
Inductor Voltage-Current Relationship
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Kirchhoff's Current Law
Kirchhoff's Current Law
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Series Circuit
Series Circuit
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Parallel Circuit
Parallel Circuit
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Voltage Divider
Voltage Divider
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Impedance Matching
Impedance Matching
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What does Req represent?
What does Req represent?
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What is the relationship between Ceq and individual capacitances in a parallel circuit?
What is the relationship between Ceq and individual capacitances in a parallel circuit?
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How does a current divider work?
How does a current divider work?
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Study Notes
Wheatstone Bridge
- Used to measure resistance changes, ranging from 1 Ω to 1 MΩ.
- Balanced when the potential difference between points B and D is zero (voltage drop across R₁ = voltage drop across R₂).
- A gauge (G) indicates no current flow when balanced.
- Often used to measure changes in physical variables by measuring changes in output resistance of transducers.
- Leads connecting the unknown resistance (Rₓ) to the bridge should have small resistance compared to Rₓ.
Balanced Bridge Method
- When balanced, i₂R₂ = i₁R₁
- i₂ = i₃ = E / (R₂ + R₃)
- i₁ = i₄ = E / (R₁ + Rₓ)
- R₂ / R₁ = R₃ / Rₓ (or R₁/R₃ = R₂/Rₓ)
Unbalanced Bridge (Deflection Bridge Method)
- Used for measuring dynamic signals.
- Slightly unbalanced bridges are not affected by Rb, the resistance of the bridge.
- Equivalent resistance (R) of the bridge is measured by the galvanometer (G).
- For R1, R2, R3, R4, R= (R₁R₄) / (R₁ + R₄) + (R₂R₃) / (R₂ + R₃)
- Common configurations include 2-wire and 3-wire designs.
Unbalanced Bridge (Deflection Bridge Method) Using Voltage Divider Relations
- Voltage divider relations allow for calculating voltage drop across each section of the circuit.
- Effective resistance of the bridge, presented to the battery can be calculated (R0).
Impedance Matching: Power
- To maximize power transmission, the load's impedance should match the source's impedance (RL = RS).
- The formula for voltage division is VL= (RL/ (RL + RS)) VS
Impedance Matching: Signal Integrity
- Mismatched impedances (RL << RS or RL >> RS) can lead to signal loss or distortion.
- Proper circuit termination is often required to connect different devices and circuits with different impedances.
Resistor and Capacitor and Inductor Formulas
- Resistor: R = ρL/A (Resistance = resistivity x length / cross-sectional area)
- Capacitor: V(t) = (1/C)∫0tI(τ)dτ = q(t)/C, I(t) = C(dV/dt)
- Inductor: V(t) = L(dI/dt), I(t) = (1/L)∫0tV(τ)dτ
Kirchhoff's Laws
- Kirchhoff's Voltage Law (KVL): The sum of voltages around any closed loop in a circuit is zero.
- Kirchhoff's Current Law (KCL): The sum of currents entering a node (junction) in a circuit is equal to the sum of currents leaving the node.
Series and Parallel Circuits
- Series Circuit:
- Equivalent Resistance: Req = R₁ + R₂ + ... + RN
- Equivalent Capacitance: Ceq = 1/ (1/C₁ + 1/C₂ + ... + 1/CN)
- Equivalent Inductance: Leq = L₁ + L₂ + ... + LN
- Parallel Circuit:
- Equivalent Resistance: 1/Req = 1/R₁ + 1/R₂ + ... + 1/RN
- Equivalent Capacitance: Ceq = C₁ + C₂ + ... + CN
- Equivalent Inductance: 1/Leq = 1/L₁ + 1/L₂ + ... + 1/LN
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