Measurement of R/L/C Using Bridge Circuits MCQ Quiz - Objective Question with Answer for Measurement of R/L/C Using Bridge Circuits - Download Free PDF

Maxwell’s Inductance-Capacitance Bridge

Maxwell's Inductance-Capacitance Bridge uses a standard capacitor to measure an unknown inductance; it compares the unknown inductance to the known capacitance to determine its value. 

Balance Conditions:

At balance (no current through the detector), the following formulas apply:

\(R_1={R_2R_3\over R_4}\)

The value of the unknown inductance is given by:

\(L_1=R_2R_3C_4\)

De Sauty Bridge

De Sauty Bridge measures an unknown capacitance in terms of a standard capacitance, and it is suitable only for a pure capacitor. 

The unknown capacitor (C_x) is given by:

\(C_x=C({R_2\over R_1})\)

One major disadvantage of the De Sauty Bridge is that it is only accurate for perfect capacitors; it cannot accurately measure capacitors with dielectric losses, leading to inaccurate results for imperfect capacitors. 

Concept:

Low resistance measurement requires precise techniques that minimize the effect of lead and contact resistances. Common methods for such measurements include the Kelvin Double Bridge and Ammeter-Voltmeter method. However, the Loss of Charge method is typically used for measuring high insulation resistance, not low resistance.

Explanation of Methods:

- Potentiometer Method: Used for accurate low voltage and low resistance measurements.
- Loss of Charge Method: Used for high resistance or insulation resistance measurements.
- Ammeter-Voltmeter Method: Simple method for measuring low to medium resistance.
- Kelvin Double Bridge Method: Most accurate method for very low resistance measurements.

Schering Bridge

The value of the unknown capacitor C_x is given by:

\(C_x={C_2}{R_4\over R_3}\)

Calculation

Given, C2 = 500 pF, known resistor R3 = 5 kΩ

Balancing resistor R4 = 1 MΩ

\(C_x=500\times 10^{-12}\times {1\times 10^6\over 5\times 10^3}\)

C_x = 100 nF

Explanation:

Measurement of Dielectric Loss and Power Factor

Definition: Dielectric loss refers to the energy lost as heat in a dielectric material when it is subjected to an alternating electric field. The power factor is a measure of the phase difference between voltage and current in an AC circuit, indicating how effectively electrical power is being converted into useful work. The measurement of dielectric loss and power factor is crucial in the electrical and electronics industry to evaluate the efficiency and performance of insulating materials.

Correct Option: Schering Bridge

The correct method for measuring dielectric loss and power factor is by using the Schering Bridge. The Schering Bridge is a type of AC bridge circuit designed specifically for the precise measurement of the capacitance, dielectric loss, and power factor of insulating materials. Its design makes it highly suitable for evaluating the quality and performance of dielectrics.

Working Principle: The Schering Bridge operates on the principle of balancing the impedances in an AC bridge circuit. It uses known capacitances and resistances to determine the unknown capacitance and dielectric loss factor of the test material. The balance condition of the bridge is obtained when the voltage across the opposite arms is zero, allowing for accurate measurement of the desired parameters.

Advantages of Using Schering Bridge:

• Highly accurate for measuring dielectric loss and power factor.
• Simple and efficient design, specifically tailored for dielectric and insulation testing.
• Capable of measuring very small dielectric losses, making it suitable for high-quality insulation materials.
• Can be used for both laboratory testing and field measurements with appropriate modifications.

Applications of Schering Bridge:

• Testing the quality of insulating materials in cables, transformers, and capacitors.
• Measuring the power factor of dielectric materials used in electrical systems.
• Evaluating the performance of insulation in high-voltage equipment.
• Used in research and development for the design of new dielectric materials.

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Wien's Bridge

The Wien's Bridge is primarily used for measuring the frequency of an AC signal. It is not suitable for measuring dielectric loss or power factor, as its design is not intended for evaluating dielectric properties. The primary application of the Wien's Bridge is in oscillator circuits and signal processing.

Option 2: Hay's Bridge

The Hay's Bridge is used for measuring inductance, particularly for coils with high Q-factor (quality factor). It is not suitable for the measurement of dielectric loss or power factor, as it is specifically designed for inductive components rather than capacitive or dielectric materials.

Option 4: Wheatstone Bridge

The Wheatstone Bridge is a DC bridge circuit used to measure resistance. It is widely used in electrical measurements but is not designed for AC measurements or for evaluating dielectric loss and power factor. Its applications are limited to resistance measurement in low-frequency or DC circuits.

Conclusion:

Among the given options, the Schering Bridge is the most suitable and widely used instrument for the measurement of dielectric loss and power factor. Its specialized design for evaluating insulating materials makes it an essential tool in the electrical and electronics industry. While the other options serve specific purposes (frequency measurement, inductance measurement, and resistance measurement), they are not appropriate for the measurement of dielectric properties. Understanding the unique characteristics and applications of each bridge is essential for selecting the correct measurement technique in various engineering applications.

Wheatstone is used for the measurement of a medium value range of resistance from 1 Ω to a few M Ω.

Important Points

• Maxwell’s inductance-capacitance bridge is used to measure the inductance of medium-quality factor coils.
• Hay’s bridge is used to measure the inductance of high-quality factor coils.
• Anderson bridge is used to measure the low-quality factor inductance.
• Heaviside bridge is used to measure the mutual inductance.

Note:

Wheatstone Bridge:

• A Wheatstone bridge is used to measure an unknown electrical resistance.
• By balancing two legs of a bridge circuit, the unknown resistance of any one leg can be measured easily.
• It provides extremely accurate measurements.

The circuit is balanced when:  

\(\frac{R_a}{R_x}=\frac{R_1}{R_2}\)

Calculation:

Given bridge,

When R = 10 ohm:

 By bridge balance equation:

⇒\(\frac{P}{10}=\frac{Q}{S}\)

⇒\({P}=\frac{10\times Q}{S}\) ........(i)

When R is changed to 20 ohms and S is changed by 5 ohms:

By bridge balance equation:

⇒\(\frac{P}{20}=\frac{Q}{S+5}\)

⇒\({P}=\frac{20\times Q}{S+5}\) ........(iI)

Equating equations (i) and (ii)

\(\frac{10\times Q}{S}=\frac{20\times Q}{S+5}\)

\(\frac{1}{S}=\frac{2}{S+5}\)

\(2S=S+5 \)

S = 5 Ω

De-Sauty bridge is used to measure the capacitance. And the bridge balance is obtained when both the capacitors are perfect.

Important Points:

Maxwell’s Inductance Bridge is used to measure only inductance but not for quality factor.

Maxwell’s Inductance Capacitance Bridge is used to measure inductance and quality factor below 10.

Hay’s Bridge is used to measure inductance and quality factor above 10.

Anderson’s Bridge is used to measure values of inductance and quality factor in a low range less than 1.

• Megger is a portable instrument to measure high insulation resistances
• It basically works on the principle of electromagnetic induction
• The electrical power to a megger is provided by permanent magnet D.C. generator
• The test voltages are usually of order 500, 1000, or 2500 V are generated by hand driven generator (permanent magnet D.C. generator)

Solution

Given 

• Galvanometer scale distance from mirror =0.4m
• deflection observed =44mm

Concept

the formula relating deflection, the distance of scale from the mirror, and coil turn angle is given by

⇒Deflection(d)=2 r θ_r  ,here

• d is the deflection observed
• r is the distance of scale from the mirror
• θ_r is the angle through which coil has tuned

​Calculation

⇒d=2 r θr 

⇒θ = \(\frac{d}{2r} \)

⇒θ = \(\frac{44 × 10^{-3}}{2× 0.4}\)

⇒θ = 55 × 10^-3 radian

Hence angle through which the coil turns = 55 × 10-3 rad

The correct option is 4

• Megger is a portable instrument to measure high insulation resistances
• It basically works on the principle of electromagnetic induction
• The electrical power to a megger is provided by permanent magnet D.C. generator
• The test voltages are usually of order 500, 1000, or 2500 V are generated by a hand-driven generator (permanent magnet D.C. generator)
• The operation of a megger is based on moving coil meter

Insulation resistance of a cable can be measured by the following method.

Direct deflection method (Galvanometer method):

For high resistance, such as insulation resistance of cables, a sensitive galvanometer of d'Arsonal type is used in place of the microammeter.

Many sensitive types of galvanometers can detect currents from 0.1 - 1 nA. Therefore, with an applied voltage of 1 kV, resistances are as high as 10¹² to 10 × 10¹² can be measured.

An illustration of the direct deflection method used for measuring the insulation resistance of a cable is shown in the figure below.

The galvanometer G measures the current I_R between the conductor and the metal Sheath. The leakage current I_L, over the insulating material, is carried by the guard wire wound on the insulation and therefore does not flow through the galvanometer.

Loss of Charge Method:

In 'Loss of charge method' the insulation resistance R to be measured is connected in parallel with a capacitor C and an electrostatic voltmeter.

The capacitor is charged to some suitable voltage, by means of a battery having voltage V and is then allowed to discharge through the resistance. The terminal voltage is observed over a considerable period of time during discharge.

The voltage across the capacitor at any instant t after the application of voltage is,

\({{\text{V}}_{\text{c}}} = {\text{V}}{{\text{e}}^{ - \left( {\frac{t}{{RC}}} \right)}}\)

\(\Rightarrow \frac{{{V_C}}}{V} = {{\text{e}}^{ - \left( {\frac{t}{{RC}}} \right)}}\)

\(\Rightarrow R = \frac{t}{{Cln\left( {\frac{V}{{{V_C}}}} \right)}}\)

Megger:

• It is a measuring instrument used for the measurement of the insulation resistance of an electrical system
• An electrical system degrades its quality of insulation resistance with time and various environmental conditions including temperature, moisture, dust particles & humidity
• Even mechanical and electrical stress affects the insulation resistance which adds to the necessity of checking insulation resistance at regular intervals so as to avoid fatal errors or electrical shocks
• Megger is used for measuring the electrical leakage in wires, electrical insulation levels in generators, motors, etc

Kelvin's double bridge is used for measuring low values of resistance.

Note: