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Questions and Answers

What classification do resistances of the order of 1 Q and under fall into?

  • High resistances
  • Medium resistances
  • Low resistances (correct)
  • Variable resistances
  • Which of the following methods is NOT used for measuring medium resistances?

  • Capacitor method (correct)
  • Ammeter-Voltmeter method
  • Substitution method
  • Wheatstone bridge method
  • What do high resistances classify as?

  • Resistances from 0.1 MQ and upwards (correct)
  • Resistances from 1 Q to about 0.1 MQ
  • Resistances from 0.01 Q to 1 Q
  • Resistances below 0.1 Q
  • What is a common limitation of the ammeter-voltmeter method?

    <p>The voltmeter measures the total voltage including the ammeter (A)</p> Signup and view all the answers

    Which resistance measurement technique is generally suitable for laboratory use due to instrument availability?

    <p>Ammeter-Voltmeter method (D)</p> Signup and view all the answers

    What range of resistances does the medium resistance classification cover?

    <p>From 1 Q to about 0.1 MQ (A)</p> Signup and view all the answers

    What can lead to inaccurate results when measuring resistance?

    <p>Disturbances in circuit conditions (D)</p> Signup and view all the answers

    What is the primary purpose of the Carey-Foster Slide-wire Bridge?

    <p>To determine the difference between standard and unknown resistances (C)</p> Signup and view all the answers

    What does the symbol 'l2' represent in the context of the slide-wire bridge?

    <p>The difference in length between two positions at balance (D)</p> Signup and view all the answers

    Which equation relates the resistances S and R to the lengths of the slide-wire at balance?

    <p>S - R = (l1 - l2)r (A)</p> Signup and view all the answers

    How are the resistances P and Q adjusted in relation to R and S?

    <p>So their ratio is equal to the ratio of R to S (A)</p> Signup and view all the answers

    What is eliminated from the calculations when comparing resistances S and R using the Carey-Foster Slide-wire Bridge?

    <p>The resistances of P and Q contact resistances and connecting leads (A)</p> Signup and view all the answers

    What is the calculated true value of resistance R based on the measurement Rm2?

    <p>86 Ω (A)</p> Signup and view all the answers

    What is the percentage error associated with the ammeter reading at 0.42 A?

    <p>1.19% (A)</p> Signup and view all the answers

    How is the error due to both the ammeter and voltmeter calculated?

    <p>Using their standard deviations in a formula (B)</p> Signup and view all the answers

    What is the formula used to calculate the percentage error in the voltmeter reading of 35.5 V?

    <p>(0.25 / 35.5) x 100 (A)</p> Signup and view all the answers

    What does the connecting diagram for the substitution method include?

    <p>A combination of both R and S with an ammeter (C)</p> Signup and view all the answers

    What is the formula used to determine the percentage error from the voltmeter?

    <p>(0.5/35.5)x100 (B)</p> Signup and view all the answers

    What is the percentage error calculated by combining the ammeter error of 1.19% and voltmeter error of 0.704%?

    <p>± 1.38% (C)</p> Signup and view all the answers

    Which value is not directly derived from the measured values of resistance in the calculations?

    <p>Resistance of the ammeter (A)</p> Signup and view all the answers

    What happens when the switch is toggled to position '2' in the substitution method?

    <p>S is inserted into the circuit (A)</p> Signup and view all the answers

    What is the typical accuracy range for measurements using an ordinary ohmmeter?

    <p>3% to 5% (B)</p> Signup and view all the answers

    What condition must be satisfied for a Wheatstone bridge to be considered balanced?

    <p>No current flows through the galvanometer. (A)</p> Signup and view all the answers

    Which component is typically used as a null detector in a Wheatstone bridge?

    <p>A galvanometer (D)</p> Signup and view all the answers

    What is the role of the standard resistor in the substitution method?

    <p>To provide a known reference resistance. (C)</p> Signup and view all the answers

    How does the deflection of the galvanometer relate to the total resistance in the circuit?

    <p>It is inversely proportional to the total resistance. (D)</p> Signup and view all the answers

    In the Wheatstone bridge method, which factors influence the accuracy of measurement?

    <p>The circuit's battery emf constancy. (C)</p> Signup and view all the answers

    Which of these is a characteristic of the substitution principle used in resistance measurement?

    <p>It allows direct comparison of unknown and known resistances. (B)</p> Signup and view all the answers

    Which parameters primarily affect the measurement accuracy in resistance measurements?

    <p>The sensitivity of the instrument. (D)</p> Signup and view all the answers

    When measuring high resistances, which method is commonly used instead of the standard Wheatstone bridge configuration?

    <p>A modified Wheatstone bridge. (D)</p> Signup and view all the answers

    What is the key relationship described in the formula for bridge balance, $P=I_2R$?

    <p>It indicates the balance of potentials at the bridge. (C)</p> Signup and view all the answers

    What happens to the sensitivity of a bridge circuit if the ratio P/Q is greater or smaller than unity?

    <p>Sensitivity decreases considerably. (A)</p> Signup and view all the answers

    In the Thevenin equivalent circuit, what parameters are represented in the circuit?

    <p>An emf and an internal resistance. (B)</p> Signup and view all the answers

    For a bridge with equal arms, what is the relationship between R, S, P, and Q?

    <p>R = S = P = Q (A)</p> Signup and view all the answers

    What is the effect of averaging two readings in a galvanometer circuit?

    <p>It doubles the sensitivity of the bridge. (A)</p> Signup and view all the answers

    What does the current through the galvanometer depend on?

    <p>The Thevenin equivalent circuit. (A)</p> Signup and view all the answers

    What is the effect of having a low ratio P/Q in the sensitivity of a circuit?

    <p>It reduces accuracy. (C)</p> Signup and view all the answers

    What expression relates to finding the Thevenin or open circuit voltage in a galvanometer circuit?

    <p>$£Un = E - En$ (B)</p> Signup and view all the answers

    What can be inferred about the relationship between sensitivity and accuracy in bridge circuits?

    <p>Increased sensitivity leads to decreased accuracy. (B)</p> Signup and view all the answers

    What role does the resistance of the galvanometer circuit, denoted by G, play in the measurements?

    <p>It affects the deflection observed. (A)</p> Signup and view all the answers

    If the ratio of P/Q is found to be 1000, how does it compare to unity in terms of sensitivity?

    <p>Sensitivity will decrease considerably. (B)</p> Signup and view all the answers

    Flashcards

    High resistance

    Resistances of the order of 0.1 megaohms or higher.

    Medium resistance

    Resistances from 1 ohm upwards to about 0.1 megaohms.

    Low resistance

    Resistances of the order of 1 ohm or lower.

    Ammeter-Voltmeter Method

    A method to measure resistance using an ammeter and a voltmeter.

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    Ammeter-Voltmeter Method Accuracy

    The ammeter measures the true current but the voltmeter measures the total voltage including the voltage drop across the ammeter itself.

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    Substitution Method

    A method to find resistance by replacing the unknown resistor with a known one and adjusting until the same current flows.

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    Wheatstone Bridge Method

    The Wheatstone bridge is a precise circuit used to measure unknown resistances.

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    Percentage Error

    The difference between the measured value and the true value of a quantity, expressed as a percentage of the true value.

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    Measured Resistance (Rm)

    The resistance of a component measured directly using a voltmeter and ammeter.

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    True Resistance (R)

    The actual or true value of a resistance, often determined using a more precise method.

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    Combining Errors

    A method to calculate the overall error in a measurement by combining the individual errors of each component.

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    Standard Variable Resistance

    A type of resistance that has a variable value, allowing you to adjust the amount of resistance in a circuit.

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    Error in Measurement

    The difference between the true value and the value measured in the experiment.

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    Measurement

    The process of determining how much or how often something is being measured, including the precision and accuracy of the measurement.

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    Factors affecting resistance measurement accuracy

    The accuracy of a resistance measurement depends on factors like the stability of the battery's voltage, the resistance of the circuit excluding the unknown resistance, the sensitivity of the measuring instrument, and the accuracy of the standard resistance used.

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    Points 'c' and 'd' in a Wheatstone bridge

    In a Wheatstone bridge, the points where the bridge is believed to be balanced are called ‘c' and ‘d'. The potential difference between these points determines the current flow through the galvanometer.

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    Wheatstone bridge balance condition

    When no current flows through the galvanometer in a Wheatstone bridge, indicating a balanced state, this happens when the potential difference between points 'c' and 'd' is zero.

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    Voltage drop relationship in balanced Wheatstone bridge

    The voltage drop across the standard resistor (P) is equal to the voltage drop across the unknown resistor (R) when the Wheatstone bridge is balanced. This relationship is based on the current and the resistance values.

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    Wheatstone bridge accuracy for medium resistances

    The Wheatstone bridge is a common and accurate method for measuring medium resistances, offering much higher precision compared to other methods like the standard ohmmeter.

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    Galvanometer sensitivity and accuracy

    The sensitivity of the galvanometer is a crucial factor in the Wheatstone bridge's accuracy: a more sensitive galvanometer can detect even smaller current variations, leading to more precise measurements.

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    Substitution method's applications

    The substitution method, despite its simplicity, is a valuable technique used in various applications like bridge methods and high-frequency AC measurements. Its core principle involves comparing known and unknown quantities to determine the unknown.

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    Wheatstone bridge components

    The Wheatstone bridge is a circuit with four resistive arms (P, Q, R, and S). A battery provides the power source, and a galvanometer acts as a null detector to determine balance.

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    Carey-Foster Slide-wire Bridge

    A method used to compare two nearly equal resistances by adjusting the position of a sliding contact on a slide-wire to achieve balance.

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    Balance Point

    The point at which the current through the galvanometer in a bridge circuit is zero, signifying that the voltage across the bridge is equal.

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    Difference between Standard and Unknown Resistances

    The ratio of the resistance per unit length of the slide-wire to the difference in lengths at balance.

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    Slide-wire Calibration

    The process of determining the resistance per unit length of the slide-wire by shunting a known resistance and measuring the change in balance length.

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    Standard Resistance

    A known resistance used for comparison with an unknown resistance in a bridge circuit.

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    Sensitivity of a Wheatstone Bridge

    The sensitivity of a Wheatstone bridge decreases significantly when the ratio of resistances (P/Q and R/S) deviates from unity (1). This means the bridge becomes less responsive to changes in the unknown resistance.

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    Thevenin Equivalent Circuit for a Wheatstone Bridge

    A Thevenin equivalent circuit simplifies a complex circuit into a voltage source (emf) and an internal resistance. This allows for easier analysis of the current flowing through the galvanometer in a Wheatstone bridge.

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    Open-Circuit Voltage (E0)

    The open-circuit voltage between terminals b and d in a Wheatstone bridge, measured when the galvanometer circuit is open. It represents the potential difference that drives the current through the galvanometer.

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    Thevenin Resistance (R0)

    The internal resistance of the Thevenin equivalent circuit of a Wheatstone bridge. It represents the resistance encountered by the galvanometer current.

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    Galvanometer Current

    The current flowing through the galvanometer in a Wheatstone bridge. This current is directly proportional to the imbalance in the bridge and helps determine the unknown resistance.

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    Current Reversal Method

    A method to eliminate the effects of thermo-electric emfs in resistance measurements. This is done by taking two readings with the current direction reversed and averaging the results.

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    Sensitivity Enhancement with Current Reversal

    The sensitivity of a Wheatstone bridge can be doubled by using the current reversal method. This is because the errors from thermo-electric emfs are effectively removed, allowing for a more precise measurement.

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    Temperature Effects on Resistance

    Temperature changes can affect the resistance values in the Wheatstone bridge, influencing the accuracy of the measurement. It's crucial to minimize temperature variations during the measurement.

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    Sensitivity of a Balanced Wheatstone Bridge

    In a Wheatstone bridge with perfectly balanced arms (R=S=P=Q), the sensitivity of the bridge is maximized. This means even small changes in resistance are easily detectable.

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    Study Notes

    Measurement of Resistance

    • Low resistances are those of 1 Ω or less.
    • Medium resistances range from 1 Ω to 0.1 MΩ.
    • High resistances are above 0.1 MΩ.
    • Different measurement techniques are used for each class.

    Measurement of Medium Resistances

    • Ammeter-Voltmeter Method:

      • Used for measuring medium resistances.
      • Two types of connections shown (Fig. 14.1(a) and 14.1(b)).
      • Accurate measurements require ammeter resistance to be zero and voltmeter resistance to be infinite.
      • In reality, these ideal conditions are not met
      • Measured resistance is higher than true resistance because of ammeter resistance.
      • Measured value = True value + Ammeter resistance.
      • Relative error is equal to (Measured - True)/True).
      • This method is popular in labs because these instruments are available.
    • Substitution Method:

      • More accurate than the ammeter-voltmeter method.
      • Errors are reduced by keeping the battery emf constant.
    • Wheatstone Bridge Method:

      • A very important instrument extensively used.
      • Measures resistances to high accuracy.
      • It utilizes a null indication principle.
    • Ohmmeter Method

      • Not explained in detail.

    Additional Notes

    • Accuracy of measurements is affected by the resistance of the measuring instruments.
    • Errors are minimized when the resistance being measured is significantly larger than the instrumentation resistance.
    • The suitability of a method depends on the values of resistance under measurement and the instrument resistances.

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