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

Megger

A Megger (Megohmmeter) measures high insulation resistance in electrical circuits. It consists of:

• Current Coil (1 Coil): Produces torque proportional to the current flowing.
• Potential Coils (2 Coils): Produces torque proportional to the applied voltage.

The interaction between these coils ensures accurate insulation resistance measurement.

Construction of Megger

• The Megger has one current coil and two voltage coils V₁ and V₂.
• The voltage coil V₁ is passed over the magnet connected to the generator.
• When the pointer of the PMMC instrument deflects towards infinity, it means that the voltage coil remains in the weak magnetic field and thus experienced very little torque.
• The torque experienced by the coil increases when it moves inside the strong magnetic field.
• The coil experiences the maximum torque under the pole faces and the pointer is set at the zero ends of the resistance scale.
• To improve the torque, the voltage coil V₂ is used.
• The coil V₂ is so allocated that when the pointer deflects from infinity to zero, the coil moves into a stronger magnetic field.
• In Megger, the combined action of both the voltage coils V₁ and V₂ are considered.
• The coil comprises a spring of variable stiffness. It is stiff near the zero ends of the coil and becomes very weak near the infinity end of the spring.

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: