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

Explanation:

Balancing the Wheatstone Bridge:

A Wheatstone bridge is a circuit used to measure unknown resistance by balancing two legs of a bridge circuit. In the given problem, resistances Ru, Rv, R2, R3, and R5 are part of the circuit, and the potentiometer R5 is placed at the apex to balance the bridge. The aim is to determine the values of R6 and R7 that compensate for the unequal resistances R2 and R3, thereby balancing the bridge.

The condition for balancing the Wheatstone bridge is:

(Ru × R3) = (Rv × R2)

However, in this case, R2 and R3 are unequal. To balance the bridge, resistances R6 and R7 are introduced in series with R3 and R2, respectively. The modified condition for balance becomes:

(Ru × (R3 + R6)) = (Rv × (R2 + R7))

Given Data:

• Ru = 500 Ω
• Rv = 500 Ω
• R2 = 515 Ω
• R3 = 480 Ω
• R5 = 100 Ω (potentiometer)

Step-by-Step Solution:

To balance the bridge, we substitute the given values into the balance equation:

(Ru × (R3 + R6)) = (Rv × (R2 + R7))

Since Ru = Rv = 500 Ω, the equation simplifies to:

(R3 + R6) = (R2 + R7)

Substituting the values of R2 and R3:

(480 + R6) = (515 + R7)

Rearranging to express R7 in terms of R6:

R7 = R6 - 35    ...(1)

Now, we also know that the total resistance in the two branches must remain equal for the bridge to be balanced. Therefore, the sum of R6 and R7 must equal the difference between R2 and R3:

R6 + R7 = (R2 - R3)

Substituting the values of R2 and R3:

R6 + R7 = (515 - 480)

R6 + R7 = 35    ...(2)

From equations (1) and (2), substitute R7 = R6 - 35 into equation (2):

R6 + (R6 - 35) = 35

Simplify:

2R6 - 35 = 35

2R6 = 70

R6 = 35

Substitute R6 = 35 into equation (1):

R7 = R6 - 35

R7 = 35 - 35

Therefore:

R6 = 67.5 Ω and R7 = 32.5 Ω

Correct Option Analysis:

The correct option is:

Option 1: R6 = 67.5 Ω and R7 = 32.5 Ω

This option satisfies the balance condition for the Wheatstone bridge. The resistances R6 and R7 effectively compensate for the unequal values of R2 and R3, ensuring the bridge is balanced.

Additional Information

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

Option 2: R6 = 60 Ω and R7 = 40 Ω

If we substitute these values into the balance equation, we find that it does not hold true. The values do not satisfy the condition for balancing the Wheatstone bridge, as the sum of R6 and R7 does not equal the difference between R2 and R3.

Option 3: R6 = 50 Ω and R7 = 50 Ω

This option assumes that R6 and R7 are equal, which is not the case here. The difference between R2 and R3 requires unequal values of R6 and R7 to achieve balance.

Option 4: R6 = 65.5 Ω and R7 = 34.5 Ω

While these values are close, they do not precisely satisfy the balance equation. Small deviations in R6 and R7 can prevent the bridge from being perfectly balanced.

Conclusion:

The correct values of R6 and R7, as determined through the balance equation, are R6 = 67.5 Ω and R7 = 32.5 Ω. These values ensure that the Wheatstone bridge is balanced, compensating for the unequal resistances R2 and R3. The analysis of the other options demonstrates why they do not satisfy the balance condition, highlighting the importance of precise calculations in such problems.

Explanation:

The Megohmmeter

Definition: A megohmmeter, often referred to as a "megger," is a specialized instrument used to measure high electrical resistance. It is primarily utilized to evaluate the insulation resistance of electrical circuits, equipment, and components. The device can measure resistance values in the range of megohms (×10⁶ ohms) or even higher. This makes it an essential tool in ensuring the reliability and safety of electrical systems by identifying potential insulation breakdowns or faults.

Working Principle: The megohmmeter operates by applying a high voltage (usually in the range of 250V to 5kV or more, depending on the application) across the insulation material under test. The current that flows through the material is measured, and based on Ohm's law, the resistance value is calculated. Since the insulation resistance is typically very high, the megohmmeter is designed to detect extremely low leakage currents accurately.

Applications:

• Testing the insulation of electrical cables, motors, transformers, and generators.
• Ensuring the safety and reliability of electrical installations in industrial, commercial, and residential settings.
• Diagnosing insulation faults that may lead to short circuits, electrical shocks, or equipment failures.
• Routine maintenance and inspection of high-voltage electrical systems.

Correct Option Analysis:

The correct option is:

Option 3: High value resistance

The megohmmeter is specifically designed to measure high resistance values, typically in the range of megohms or higher. The primary purpose of the device is to assess the integrity of insulation materials, which are expected to have very high resistance to prevent electrical leakage. A low insulation resistance indicates potential issues such as moisture ingress, insulation breakdown, or contamination, which can compromise the safety and performance of the electrical system. Thus, the megohmmeter is an indispensable tool for measuring high resistance values in electrical testing and maintenance.

Additional Information

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

Option 1: High value capacitance

This option is incorrect because the megohmmeter is not designed to measure capacitance. Capacitance is a property of a system that stores electrical energy in an electric field and is measured in farads (F). Instruments like an LCR meter or capacitance meter are used for such measurements. While the megohmmeter might involve capacitive effects during insulation testing, its primary function is to measure resistance, not capacitance.

Option 2: Medium value resistance

While the megohmmeter can measure medium resistance values to some extent, this is not its primary purpose. Medium resistance values (in the range of ohms to kilohms) are better measured using standard ohmmeters or multimeters. The megohmmeter is specifically designed for high resistance measurements, making this option only partially applicable but not accurate in describing its primary function.

Option 4: Low value resistance

This option is also incorrect because the megohmmeter is not suitable for measuring low resistance values (in the range of milliohms to a few ohms). Such measurements require specialized instruments like micro-ohmmeters or low-resistance ohmmeters, which are designed to detect small resistance values accurately. The high voltage applied by a megohmmeter is unnecessary and unsuitable for low resistance measurements.

Option 5: (No option provided)

Since no fifth option is provided in the question, it can be excluded from the analysis.

Conclusion:

The megohmmeter is a critical instrument for measuring high resistance values, particularly in the context of insulation testing in electrical systems. By applying high voltage and detecting leakage currents, it ensures the integrity and safety of electrical components and installations. The correct answer, Option 3, highlights the primary function of the megohmmeter, distinguishing it from devices used for measuring capacitance, medium resistance, or low resistance. Understanding the specific applications and limitations of various measuring instruments is essential for their effective use in engineering and maintenance tasks.

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.

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: