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Questions and Answers

What effect do leadwire resistances have in a strain gage bridge configuration?

  • They add to the total resistance of the strain gage branch. (correct)
  • They reduce the efficiency of the circuit.
  • They do not affect the resistance at all.
  • They create an additional voltage source.
  • How does a three-wire connection assist in strain gage bridges?

  • It increases the current flowing through the circuit.
  • It offset changes in leadwire resistances. (correct)
  • It eliminates all resistance from the circuit.
  • It doubles the voltage from the strain gage.
  • What is the primary role of a capacitor in a circuit?

  • To allow direct current to flow continuously.
  • To store energy in the form of an electric field. (correct)
  • To increase the overall resistance in the circuit.
  • To store energy in the form of a magnetic field.
  • According to Ohm's law, what does the equation V = IR represent?

    <p>The relationship between voltage, current, and resistance. (C)</p> Signup and view all the answers

    What determines the resistance of a wire according to the formula R = ρL/A?

    <p>The length of the wire and its cross-sectional area. (B)</p> Signup and view all the answers

    What is the formula for calculating the equivalent resistance in a series circuit?

    <p>Req = R1 + R2 + ... + RN (B)</p> Signup and view all the answers

    What does Faraday's law of induction relate to in an inductor?

    <p>The change in voltage and current. (A)</p> Signup and view all the answers

    Which law states that the sum of the currents flowing into a closed surface or node is zero?

    <p>Kirchhoff's current law (B)</p> Signup and view all the answers

    What is the general form of the voltage divider equation for a resistor Ri?

    <p>VRi = Vs * (Ri / (R1 + R2)) (A)</p> Signup and view all the answers

    Which of the following statements best describes Kirchhoff's voltage law?

    <p>The sum of voltages around a closed loop is zero. (D)</p> Signup and view all the answers

    What is the typical range of capacitance for capacitors?

    <p>1 pF to 1000 uF (D)</p> Signup and view all the answers

    How do you find the equivalent capacitance of capacitors in series?

    <p>Ceq = 1 / (1/C1 + 1/C2) (A)</p> Signup and view all the answers

    In a parallel circuit, how is the equivalent resistance calculated?

    <p>1 / Req = 1/R1 + 1/R2 + ... + 1/RN (A)</p> Signup and view all the answers

    What is the condition to maximize power transmitted to the load in an impedance matching scenario?

    <p>RL should equal Rs (B)</p> Signup and view all the answers

    Which equation represents the power transmitted to the load in an impedance matching scenario?

    <p>PL = (VL^2) / RL (A)</p> Signup and view all the answers

    What describes a current divider in a parallel circuit?

    <p>I1 = I * (R2 / (R1 + R2)) (A)</p> Signup and view all the answers

    What is the main function of a Wheatstone bridge?

    <p>To measure resistance changes (D)</p> Signup and view all the answers

    In a balanced Wheatstone bridge, what does the galvanometer indicate?

    <p>No current flow (A)</p> Signup and view all the answers

    Which method is used for measuring dynamic signals with a Wheatstone bridge?

    <p>Deflection Bridge Method (C)</p> Signup and view all the answers

    What characteristic is assumed for the resistances in the Wheatstone bridge for simplification?

    <p>All resistances are initially equal (A)</p> Signup and view all the answers

    What happens to the effective bridge resistance when the Wheatstone bridge is slightly unbalanced?

    <p>It remains unchanged (B)</p> Signup and view all the answers

    Which variable represents the voltage impressed on the bridge in an unbalanced condition?

    <p>Eb (B)</p> Signup and view all the answers

    In voltage divider relations, what does VA represent?

    <p>Voltage drop across R1 (B)</p> Signup and view all the answers

    If the resistance R1 changes by an amount ΔR1, what formula describes the change in electromotive force (Eg)?

    <p>Eg = E*((R1 + ΔR1)R3 - R2R4) / (R1 + R4)(R2 + R3) (D)</p> Signup and view all the answers

    What effect do long leadwires have in a Wheatstone bridge setup?

    <p>Increase the total resistance (B)</p> Signup and view all the answers

    Which variable is typically used to represent the effective resistance as presented to the galvanometer in an unbalanced Wheatstone bridge?

    <p>Ro (B)</p> Signup and view all the answers

    Flashcards

    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

    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

    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

    A device that converts a physical quantity (like pressure, temperature, or strain) into a change in resistance, which can be measured by the Wheatstone bridge.

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    Deflection Bridge

    A Wheatstone bridge that is slightly unbalanced, where the voltage difference between two points is not zero. The deflection is used to measure the change in the unknown resistance.

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    Effective Resistance

    The resistance presented to the galvanometer when the bridge is unbalanced. It combines the resistances of the bridge and the unknown resistance.

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    How does a Wheatstone Bridge measure resistance?

    By balancing the bridge with known resistances, the unknown resistance can be determined. When the bridge is balanced, the voltage difference between two points is zero, meaning the unknown resistance is equal to the calculated value based on the known resistances.

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    What is the difference between a balanced and unbalanced bridge?

    A balanced bridge has zero voltage difference between specific points, indicating the unknown resistance is measured. An unbalanced bridge has a voltage difference, meaning the unknown resistance is changing and the bridge is measuring the change.

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    Why are leadwire resistances important in Wheatstone Bridge measurements?

    If the leadwire resistance is significant compared to the unknown resistance, it can introduce errors in the measurement. Ideally, the leadwires should have negligible resistance compared to the measured resistance to ensure accurate readings.

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    What is the application of the Wheatstone Bridge in dynamic signal measurement?

    An unbalanced Wheatstone bridge can be used to measure dynamic signals (changing values). When a signal causes a change in the unknown resistance, the bridge becomes slightly unbalanced, producing a voltage difference proportional to the signal.

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    Leadwire Resistance Effects

    Changes in leadwire temperature affect the resistance of the bridge branch, potentially changing the output voltage.

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    Three-Wire Connection Advantage

    A three-wire connection compensates for leadwire resistance changes by adding equal resistance to adjacent branches, minimizing the effect on the output voltage.

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    Resistance Formula

    The resistance of a material is directly proportional to its resistivity, length, and inversely proportional to its cross-sectional area.

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    Ohm's Law

    The voltage across a conductor is directly proportional to the current flowing through it and the resistance of the conductor.

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    Capacitor Function

    A capacitor stores energy in an electric field by accumulating charge on its plates.

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    Capacitor Voltage-Current Relationship

    The capacitor's voltage is proportional to the integral of its current over time, or its current is proportional to the rate of change of its voltage.

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    Inductor Function

    An inductor stores energy in a magnetic field by creating a magnetic flux through its coil windings.

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    Inductor Voltage-Current Relationship

    The inductor's voltage is proportional to the rate of change of its current, or its current is proportional to the integral of its voltage over time.

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    Kirchhoff's Current Law

    The sum of currents entering a node or closed surface is always zero. This means that the total current flowing into a point is equal to the total current flowing out.

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    Series Circuit

    A circuit where components are connected end-to-end, forming a single path for current flow. The total resistance is the sum of individual resistances.

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    Parallel Circuit

    A circuit where components are connected side-by-side, providing multiple paths for current flow. The reciprocal of the total resistance is the sum of the reciprocals of individual resistances.

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    Voltage Divider

    A circuit that divides a voltage source into smaller, proportional voltages across different resistors. The voltage across a resistor is proportional to its resistance in relation to the total resistance.

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    Impedance Matching

    Optimizing the transfer of power from a source to a load by ensuring the load resistance matches the source resistance. This maximizes power transfer efficiency.

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    What does Req represent?

    Req represents the equivalent resistance of a circuit. It simplifies the circuit analysis by representing the combined effect of multiple resistors as a single equivalent resistance.

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    What is the relationship between Ceq and individual capacitances in a parallel circuit?

    In a parallel circuit, the equivalent capacitance (Ceq) is equal to the sum of the individual capacitances. This means that the overall capacitance increases with the addition of more capacitors in parallel.

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    How does a current divider work?

    A current divider divides the total current flowing into a parallel circuit into smaller currents flowing through each branch of the circuit. The current through a branch is inversely proportional to its resistance.

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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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