Extension Ranges of Basic Meters MCQ Quiz - Objective Question with Answer for Extension Ranges of Basic Meters - Download Free PDF

Explanation:

Problem Statement:

A 1mA D'Arsonval movement has a resistance of 100 Ω, and it needs to be converted into a 10 V voltmeter. The problem requires us to determine the value of the multiplier resistance for this conversion.

To solve this, we use the concept of a series resistor (multiplier resistor) to extend the voltage range of the D'Arsonval galvanometer. The following explanation provides the detailed solution:

Solution:

When designing a voltmeter using a galvanometer, a multiplier resistor is connected in series with the galvanometer. The multiplier resistor ensures that the galvanometer does not exceed its current rating while measuring higher voltages. The total resistance of the voltmeter circuit limits the current through the galvanometer to its full-scale deflection current.

Given Data:

• Full-scale deflection current of the D'Arsonval movement, I_fs = 1 mA = 1 × 10^-3 A
• Internal resistance of the galvanometer, R_g = 100 Ω
• Voltage to be measured, V = 10 V

Formula:

The total voltage across the voltmeter is shared between the galvanometer and the multiplier resistance. Mathematically, this relationship can be expressed as:

V = I_fs × (R_g + R_m)

Where:

• R_m is the multiplier resistance to be calculated.

Rearranging the equation to solve for R_m:

R_m = (V / I_fs) - R_g

Substitute the values:

R_m = (10 / 1 × 10^-3) - 100

R_m = 10,000 - 100

R_m = 9,900 Ω

Conclusion:

The value of the multiplier resistance required to convert the 1mA D'Arsonval movement into a 10V voltmeter is 9,900 Ω. Thus, the correct option is:

Option 3: 9,900 Ω

Important Information

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

Option 1: 999 Ω

This value is much lower than the calculated multiplier resistance. A multiplier resistor of 999 Ω would result in a much higher current flowing through the galvanometer, exceeding its full-scale deflection current, potentially damaging the galvanometer.

Option 2: 9,999 Ω

Although close to the correct value, this option is slightly higher than the required resistance of 9,900 Ω. Using a resistance of 9,999 Ω would limit the current to less than 1 mA, leading to an underestimation of the measured voltage.

Option 4: 990 Ω

This value is far too low, similar to Option 1. A resistance of 990 Ω would result in excessive current through the galvanometer, well beyond its full-scale deflection current, potentially causing damage.

Key Points:

• The purpose of the multiplier resistance is to ensure that the galvanometer operates within its safe current range while accurately measuring higher voltages.
• The formula R_m = (V / I_fs) - R_g is crucial for designing voltmeters using galvanometers.
• It is essential to choose the correct multiplier resistance to avoid inaccurate readings or damage to the galvanometer.

Extension of moving iron voltmeter

The range of a moving iron voltmeter can be extended by using a high value of multiplier resistance connected in series with a voltmeter.

Additional Information

Extension of moving iron ammeter 

The range of a moving iron ammeter can be extended by using a low value of shunt resistance connected in parallel with an ammeter.

Current divider rule

When two resistances are connected in parallel, the current is divided as:

Calculation

The current across R is given by:

The voltage across R is given by:

V = I₁ × R

R = 111.11 Ω

Explanation:

Extending the Range of Electrostatic Voltmeters

Definition: An electrostatic voltmeter is a type of voltmeter that measures the potential difference (voltage) between two points by using the electrostatic forces between charged plates. These voltmeters are particularly useful for measuring high voltages without drawing any current from the source.

Working Principle: Electrostatic voltmeters operate based on the principle of electrostatic force. When a voltage is applied between two plates, an electrostatic force is generated, causing the plates to move. The movement is proportional to the voltage applied, and this displacement is measured to determine the voltage.

Extending the Range: The range of an electrostatic voltmeter can be extended using several methods. The correct method, as mentioned in the question, involves using a Resistance Potential Divider.

Applications: Resistance Potential Dividers are widely used in high-voltage measurement applications, such as in power systems, high-voltage laboratories, and electrical substations

Shunt-type ammeter

A shunt-type ammeter is a device used to measure high currents by diverting most of the current through a shunt resistor and allowing only a small portion of the current to pass through the measuring instrument. This setup protects the sensitive meter from excessive currents, which could damage it.

Purpose of Swamping Resistance:

• The swamping resistance is used to minimize the effect of temperature changes on the instrument's readings.
• The material used for the moving coil (usually copper) has a high temperature coefficient of resistance, meaning its resistance changes significantly with temperature.
• To compensate for this, a swamping resistance made of a material with a low-temperature coefficient (like manganin) is added in series with the moving coil.

Working:

• By placing the swamping resistance in series, the overall resistance of the meter (moving coil + swamping resistance) becomes less sensitive to temperature variations. This is because the swamping resistance dominates the total resistance, and its value remains stable even as the temperature changes.
• This ensures that the current flowing through the ammeter (and thus the reading) does not change significantly due to temperature fluctuations, improving measurement accuracy.

Concept:

A galvanometer can be converted into an ammeter by connecting a low resistance in parallel.

The effective resistance of device = R_sh in parallel with R_g

Where R_g is galvanometer resistance

A galvanometer can be converted into a voltmeter by connecting a high resistance in series.

The effective resistance of device = R_se in series with R_g

Where R_g is galvanometer resistance

Application:

The voltmeter has high resistance and ammeter has low resistance.

Voltmeter with high full-scale range has high resistance.

So, a voltmeter of range 10 V has higher resistance.

The correct answer is option 2):(2 A and 0 V)

Concept:

The resistance of the ideal ammeter is zero

When two resistors are connected in series the total resistance will be the sum of individual resistors

The current I =

Calculation:

Given

R =  2+ 3 = 5

I = 

=  = 2A

The voltmeter is connected across the ammeter so there is a voltage drop in the ammeter because The resistance of the ideal ammeter is zero

Voltmeter reads zero.

In the circuit shown below, the reading of the ideal ammeter and voltmeter, respectively, will be 2 A and 0 V.

Concept:

We can extend the range of ammeter by keeping a shunt resistance.

Here Rm = internal resistance of the coil

Rsh = Shunt resistance

I = Required full-scale range

Im = Full scale deflection of current

As the two resistances, Rm and Rsh are in parallel, the voltage drop across the resistance is equal.

Where 

‘m’ is called multiplying power

Calculation:

Given that,

Full-scale deflection voltage (Vm) = 50 mV

Full scale deflection current (Im) = 10 mA

Meter resistance (Rm) = 50/10 = 5 Ω

Required full scale reading (I) = 5 A

Note:

To increase the ranges of ammeter, we need to connect a small shunt resistance in parallel with ammeters.

To increase the ranges of a voltmeter, we need to connect a high series of multiplier resistance in series with voltmeters.

Concept:

To increase the ammeter range, we need to add shunt resistance and it is given by

Where Rsh = shunt resistance

Rm = meter internal resistance

m = multiplier value

To increase the voltmeter range, we need to add series resistance and it is given by

Rse = Rm (m-1)

Rse = series resistance

Calculation:

Given that,

Rm = 50 Ω

Ifsd = 25 mA

Vfsd = 25 × 50 = 1250 mV

Series resistance 

Extension of ammeters:

• Shunts are used for the range extension of ammeters.
• A shunt is a low-value resistance having minimum temperature co-efficient.
• It is connected in parallel with the ammeter whose range is to be extended. The combination is connected in series with the circuit whose current is to be measured.
• Shunt provides a path for extra current as it is connected across (in parallel with) the instrument.
• These shunted instruments can be used to measure currents many times greater than their normal full-scale deflection currents.
• The ratio of maximum current (with shunt) to the full-scale deflection current (without shunt) is known as the ‘multiplying power’ or ‘multiplying factor’ of the shunt.

In the figure

I is total current flowing in the circuit

Ish is the current through the shunt resistor

Rm is the ammeter resistance

Additional Information

Extension of voltmeter: 

For range extension of voltage measurement in moving coil instrument, a resistance is connected in series with coil resistance.

Because, for a constant value of current, resistance connected in series connection has a higher voltage drop compared to a parallel or shunt connection.

The value of the series resistance is given by:

Rse = Rm (m – 1)

m = Multiplying factor = (Required full scale deflection) / (Initial full scale deflection)

Concept:

The total internal resistance of a voltmeter is given by

The sensitivity (S) of a voltmeter is the reciprocal of full-scale deflection current (Ifsd)

Rm = full scale range of voltmeter × sensitivity

Rm = Vfsd × S

Let the given voltmeter is ideal so that the resistance of the voltmeter is infinity.

Now by applying the Voltage division rule in the circuit diagram given in the question.

V1 = voltage across R1 resistance

V2 = voltage across R2 resistance

V = Total voltage

Calculation:

Given: Vfsd = 2 V, Sensitivity (s) = 1 kΩ /V

We know that, 

R_m = Vfsd × S 

R_m = 2 × 1 kΩ /V = 2 kΩ 

This 2kΩ in parallel with the 1kΩ,

so parallel equivalent resistance is,

R_parallel =  (2 × 1)/3 = 0.666 kΩ 

Now this resistance in series with 100kΩ, 

By using the voltage division rule, we can find out the voltage across the voltmeter.

So, Voltage across the voltmeter V = 

V₂ =  = 0.66 

V₂ = 0.66 V

Shunts are used for the range extension of ammeters.

• A shunt is a low-value resistance having minimum temperature co-efficient.
• It is connected in parallel with the ammeter whose range is to be extended. The combination is connected in series with the circuit whose current is to be measured.
• Shunt provides a path for extra current as it is connected across (in parallel with) the instrument.
• These shunted instruments can be used to measure currents many times greater than their normal full-scale deflection currents.
• The ratio of maximum current (with shunt) to the full-scale deflection current (without shunt) is known as the ‘multiplying power’ or ‘multiplying factor’ of the shunt.

In the figure

I = Total current flowing in the circuit

Ish = The current through the shunt resistor

Rm = The ammeter resistance

And, R_sh = 

Where, m = I/I_sh

Rsh is Shunt Resistance connecting in parallel with Ammeter

Application:

We have,

Rm = 100 Ω

I_m = 1 mA

I = 100 mA

Hence,

m = 

From above concept,

Rsh =  =  = 1.01 Ω

Loading effect:

• When a voltmeter having an internal resistance of Rm is connected in parallel with load resistance RL of circuit under test, the circuit conditions will be altered.
• The effective resistance will be the parallel combination of RL and Rm. The voltmeter indicates the voltage across this effective resistance, where the indicated voltage will always be less than true voltage. This is known as loading effect.
• Hence the instrument must possess high input impedance to reduce loading effect.

Given that, current through meter (I_m) = 100 A

Total required current (I) = 500 A

Meter resistance (R_m) = 0.1 Ω

Shunt resistance =

Concept:

• For range extension of voltage measurement in moving coil instrument, a resistance is connected in series with coil resistance.
• Because for a constant value of current, resistance connected in series connection has a higher voltage drop compared to parallel or shunt connection.
• For range extension of current measurement in moving coil instrument, a resistance is connected in parallel or shunt with coil resistance.
• Because for a constant value of voltage, resistance connected in parallel connection has a higher value of current flow compared to series connection.

Formula:

R_se = R_m(M – 1)

M= multiplying factor = (Required full scale deflection)/(Initial full scale deflection)

Where,

R_sh = Series resistance

R_m = Meter resistance

V_m = Potential difference across meter = Im × Rm

I_m = Meter current

Calculation:

Given that, 

Rm = 10 ohms

Im = 100 mA

∴ V_m = 10 × 100 × 10^-3 = 1 volt

R_se = 10 (500 – 1) = 4990