## Measurement of resistance [Learn ALL methods easily]

Hello friends, in this blog article we will learn different methods for the measurement of resistance. We will first see, what are the different types of methods in short and will explain the same in details in separate blog articles.

## Measurement of Resistance

Before learning different types of methods for measurement of resistance, we will first see the classification of resistance. From the point of view of measurement, we have three types of resistances as follows:

1. Low resistance: < 1Ω
2. Medium resistance: 1Ω to 100,000Ω
3. High resistance: >100,000Ω

### A. Measurement of Low resistance

This is a very popular method for measurement of medium resistances since instruments required for this method are usually available in the laboratory.

2. Kelvin’s double bridge method: The Kelvin double bridge is the modification of the Wheatstone bridge and provides greatly increased accuracy in measurement of low-value resistance.

3. Potentiometer method: The potentiometer is extensively used for calibration of voltmeters and ammeters and has, in fact, become the standard for the calibration of these instruments.

4. Ducter

### B. Measurement of Medium resistance

1. Ammeter-Voltmeter method

2. Substitution method: This is a more accurate method than ammeter-voltmeter method. The accuracy of this method is greatly affected if the emf of the battery changes during the time of readings.

3. Wheatstone bridge method: Another method of measuring the value of a resistor is the Wheatstone bridge. This device sets up a parallel resistor system that measures the differences in voltage between two legs of a circuit. If there is a difference of voltage between the branches it will be detected by the galvanometer.

4. Ohmmeter method

### C. Measurement of High resistance

1. Direct deflection method: Direct deflection method for measurement of high resistance

2. Loss of Charge method: In the loss of charge method unknown resistance is connected in parallel with the capacitor and electrostatic voltmeter. The capacitor is initially charged to some suitable voltage by means of a battery of voltage V and then allowed to discharge through the resistance.

3. Megohm bridge: Megohm bridge is another important method for measurement of high resistances. It has one three terminal high resistance located in one arm of the bridge.

4. Megger: We know that the ratiometer ohmmeters may be designed to cover a wide range of resistances. The principle of ratiometer ohmmeters is particularly adapted to application in portable instruments measuring insulation resistance. This principle forms the basis of insulation testing instrument known as Meggar.

## Carey Foster Bridge Construction & Working Principle

Hi friends, this post provides an information about Carey Foster bridge. We will also learn how this bridge can be used to determine the resistance in detail with deriving an expression for determining resistance.

## Carey-Foster bridge Experiment

We have already seen some basic methods for measuring medium resistances. Carey foster bridge is the method used for measurement of medium resistances. Carey foster bridge is specially used for the comparison of two equal resistances. The circuit for Carey-Foster Bridge is shown in figure below. A slide wire having length L is included between R and S. resistance P and Q are adjusted so that the ratio P/Q is approximately equal to R/S. this can be achieved by sliding contact on slide wire.

Carey foster bridge circuit

### Carey Foster Bridge: Working Principle

The working principle of Carey Foster bridge is similar to the Wheatstone bridge. The potential fall is directly proportional to the length of wire.This potential fall is nearly equal to the potential fall across the resistance connected in parallel to the battery.

### Description:

Let l1 be the distance of the sliding contact from the left hand end of the slide-wire of Carey foster bridge. The resistance R and S are interchanged and balance is again obtained. Let the distance is now l2.

Let r= resistance/unit length of slide wire

For first balance,

For second balance,

Comparing,

Where l1 and l2 are balanced points when slide wire is calibrated by shunting S with a known resistance and S’ is value of S when it is shunted by a known resistance. Thus Carey foster bridge can be used to measure the medium resistance.

## Effects of temperature changes in Ammeters:

This post provides an information about effects of temperature changes in ammeters.

Ammeter

Errors due to temperature changes in ammeters can be eliminated by using the same material for both shunt and moving coil and kept at the same temperature. But in practice this method is not suitable because temperature of both parts (shunt and moving coil) does not changes at the same rate. If we use same material like copper, there is one more disadvantaging of copper that they are likely to be bulky as the resistivity of the copper is small.

So to avoid these difficulties, there is one another method in which we use swamping resistance.

The arrangement of this method is as shown in the figure. In this method we use a resistance of material having negligible temperature coefficient like mangnin and this resistance is called as ‘swamping resistance’. Its resistance is equal to 20 to 30 times the resistance of the coil used in ammeter. The swamping resistance is connected in series with the coil and shunt of mangnin is connected across this combination as shown in figure. Since copper forms a small fraction of the series combination, the proportion in which the currents would divide between the meter and the shunt would not change appreciably with the change in the temperature.

In this manner the effects of change in temperature on ammeters can be minimized.

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Anderson’s Bridge is the modification of Maxwell’s inductance-capacitance bridge. In Anderson’s bridge, a standard capacitor is used for the measurement of self-inductance. The main advantage of this method is that it can be used for the wide range of self-inductance measurement.

The following figure shows Anderson’s bridge for the balance conditions.

Let,

• L1 = Self-inductance to be measured,
• R1 = resistance of self-inductor,
• r1 = resistance connected in series with self-inductor,
• r, R2, R3, Ra = known non-inductive resistances,
• C = fixed standard capacitor.

At balance,

1)      In Anderson’s bridge, it is very easy to obtain the balance point as compared to Maxwell’s bridge.

2)      In this bridge, a fixed standard capacitor is used therefore there is no need of costly variable capacitor.

3)      This method is very accurate for measurement of capacitance in terms of inductance.

1) It is more complex as compared with Maxwell’s inductance bridge. It has more parts and hence complex in setting up and manipulate. The balance equations of Anderson’s bridge are quite complex and much more tedious.

2) An additional junction point increases the difficulty of shielding the bridge.

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## Schering Bridge (Measurement of Capacitance)

Hi friends, this post provides an information about Schering bridge which is used for measurement of capacitance. We will also see its phasor diagram, advantages and disadvantages.

The connections and phasor diagram of the Schering bridge under balance conditions are shown in figure below.

Schering Bridge Circuit
Schering Bridge Phasor Diagram

Let

• C1= capacitor whose capacitance is to be determined,
• r1 = a series resistance representing the loss in the capacitor C1
• C2 = a standard capacitor
• R3 = a non – inductive resistance
• C4 = a variable capacitor
• R4 = a variable non-inductive resistance in parallel with variable capacitor C4

Now when the Schering Bridge is balanced, then

By equating real and imaginary part of the equation we get,

Two independent balance equations are obtained if C4 and R4 are chosen as the variable elements.

The dissipation factor is given by:

Therefore values of capacitance C1 and its dissipation factor are obtained from the values of bridge elements at balance.

Permanently set up Schering bridges are sometimes arranged so that balancing is done by adjustment of R3 and C4 remaining fixed. Since R3 appears in both the balance equations and therefore there is some difficulty in obtaining balance but it has certain advantages which are explained as follows:

We know that the equation for unknown capacitance is,

In the above equation value of R4 and C2 are fixed therefore the dial resistor R3 may be calibrated to read the capacitance directly.

• 1)    The balance equation is independent of frequency.
• 2)    It is used for measuring the insulating properties of electrical cables and equipments.

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## CRO Block Diagram and Working Principle

Hi friends, in this article we will learn Cathode Ray Oscilloscope (CRO). We will see the introduction, a block diagram of CRO and CRO Working.

Every electronic circuit has multiple electronic components connected to each other. At some point in time, we need to test the working of a circuit with the help of some parameters like current, voltage, power, etc. For such kind of testing, a very commonly used electronic device is Cathode Ray Oscilloscope i.e. CRO. Lets first study the block diagram of CRO first and then we will move to Cathode Ray Oscilloscope CRO working.

## Block Diagram of CRO:

CRO is made up of different blocks such as

1. Cathode Ray Tube (CRT)
2. Vertical amplifier
3. Delay Line
4. Trigger circuit
5. Timebase generator
6. Horizontal amplifier

## CRO Working:

### 1. Cathode Ray Tube (CRT):

CRT Produces a sharply focused beam of electrons, accelerated to a very high velocity. This electron beam travels from the electron gun to the screen. The electron gun consists of filament, cathode, control grid, accelerating anodes and focusing anode. While travelling to the screen, electron beams passes between a set of vertical deflecting plates and a set of horizontal deflection plates. Voltages applied to these plates can move the beam in vertical and horizontal plane respectively. The electron beam then strikes the fluorescent material (phosphor) deposited on the screen with sufficient energy to cause the screen to light up in a small spot.

### 2. Vertical Amplifier:

The input signal is applied to the vertical amplifier. The gain of this amplifier can be controlled by VOLT/DIV knob. Output of this amplifier is applied to the delay line.

### 3. Delay Line:

The delay Line retards the arrival of the input waveform at the vertical deflection plates until the trigger and time base circuits start the sweep of the beam. The delay line produces a delay of 0.25 microsecond so that the leading edge of the input waveform can be viewed even though it was used to trigger the sweep.

### 4.Trigger (Sync.) Circuit:

A sample of the input waveform is fed to a trigger circuit which produces a trigger pulse at some selected point on the input waveform. This trigger pulse is used to start the time base generator which then starts the horizontal sweep of CRT spot from left hand side of the screen.

### 5. Time base (Sweep) Generator:

This produces a saw-tooth waveform that is used as horizontal deflection voltage of CRT. The rate of rise of a positive going part of the sawtooth waveform is controlled by TIME/DIV knob. The sawtooth voltage is fed to the horizontal amplifier if the switch is in the INTERNAL position. If the switch is in EXT. position, an external horizontal input can be applied to the horizontal amplifier.

### 6. Horizontal Amplifier:

This amplifies the saw-tooth voltage. As it includes a phase inverter two outputs are produced. Positive going sawtooth and negative going sawtooth are applied to right – hand and left – hand horizontal deflection plates of CRT.

### 7. Blanking Circuit:

The blanking circuit is necessary to eliminate the retrace that would occur when the spot on CRT screen moves from right side to left side” This retrace can cause confusion if it is not eliminate. The blanking voltage is produced by sweep generator. Hence a high negative voltage is applied to the control grid during retrace period or a high positive voltage is applied to the cathode in CRT.

When a sawtooth voltage is applied to horizontal plates and an input signal is applied to vertical plates, display of vertical input signal is obtained on the screen as a function of time.

### 8. Power Supply:

A high voltage section is used to operate CRT and a low voltage section is used to supply electronic circuit of the oscilloscope.

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Tags: Working of CRO, How CRO generates waveforms, Working principle of CRO, CRO working.

## Three voltmeter method for measurement of power:

As we know, wattmeters are used for measurement of power in inductance AC circuits, but in some cases it is not possible to use wattmeters because of their incorrect readings or sometime wattmaters may not available. So in such cases three voltmeters or three ammeter method is used for measurement of power.

### Three voltmeter method:

Following figure shows the circuit diagram for three voltmeter method.

Three voltmeter method
Three voltmeter method vector diagram

V1, V2 and V3 are the three voltmeters and R is a non-inductive resistance connected in series with the load as shown in figure.

From the phasor diagram, we have:

The assumptions are made that the current in the resistor R is same as the load current.

• Supply voltage higher than normal voltage is required because an additional resistance R is connected in series with the load Z (inductive circuit).
• Even small errors in measurement of voltages may cause serious errors in the value of power determined by this method.

Let us solve one simple numerical example based on three voltmeter method for clear understanding.

### Example 1:

The following readings were obtained from three voltmeters used for a single phase power measurement:

V2 = 180 voltas across a non-inductive resistaor; V3 = 200 volts across an inductive load; V1 = 300 volts across the two in series.

Calculate the power factor of the inductive load.

### Solution:

Given: V2 = 180 V; V3 = 200 V; V1 = 300 V

Power factor, cos ? = (V1^2 – V2^2 – V3^3)/2V2V3

Or cos ? = [(300^2) – (180^2) – (200^2)]/(2*180*200) = 0.244   (Ans.)

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## Thermal wattmeter:

Following figure shows the arrangement of thermal wattmeter for measurement of power:

Thermal Wattmeter

This wattmeter uses two similar thermocouples (1 and 2) whose outputs are connected in opposition with a galvanometer in between. Rh is the resistance of each thermocouple heating element. R is high series resistance, and between C and D is a low resistance R2 capable of carrying the load current i. the resistance R2 develops a potential difference which depends upon the load current, together with the current of one heater, and the series resistance R carries the current of both heaters.

If v be the instantaneous voltage at the load, then assuming identical thermocouples, we have:

From above two equations, we get:

e.m.f. of thermocouple 1,

If  Rh+R  is not very different from Rh, the C2*i^2 may be neglected and T(inst.) is directly proportional to v*i or instantaneous power.

Thus, galvanometer may be calibrated to read the power.

• The commercial thermal wattmeters employ a number of thermocouples connected in the form of a chain in order to increase the output. C.T.s and P.T.s are also used with these instruments.
• For high frequency measurements careful shielding is required.

The thermal wattmeters can be used for measurement of power is several circuits and the sum of their outputs can be applied to a recording potentiometer which records the total power.

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Electrostatic type Wattmeter

Dynamometer type wattmeter

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## Electrostatic Wattmeter:

These wattmeters are used for measurement of small amount of power, practically when the voltage is high and power factor is low. This type of wattmeter is also used for measurement of dielectric loss of cables on alternating voltage and for calibration of wattmeters and energy meters.

Electrostatic wattmeter consists of a quadrant electrometer used with a non-inductive resistor R as shown in figure below.

Electrostatic wattmeter

Instantaneous torque,

Instantaneous torque,

i.e. instantaneous torque is proportional to the instantaneous power in the load plus half of the power lost in noninductive resistance.

• Electrostatic wattmeter is a precision instrument and should be used as such.
• It is free from errors on account of waveforms, frequency and eddy currents.
• It has a very small working torque.

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Thermal wattmeter

Dynamometer type wattmeter

## Dynamometer Type Wattmeter – Construction and working principle

Hello friends, in this post we will see construction and working principle & classification of dynamometer type wattmeter. We will also see the advantages and disadvantages of dynamometer type wattmeter.

## Construction of Dynamometer Type Wattmeter:

The following figure shows the dynamometer wattmeter for measuring the power. If two coils are connected such that, current proportional to the load voltage, flows through one coil and current proportional to the load current, flows through another coil, the meter can be calibrated directly in watts. This is true because the indication depends upon the product of the two magnetic fields. The strength of the magnetic fields depends upon the values of the current flowing through the coils.

Working of Dynamometer Type Wattmeter:

Let us consider

• v=supply voltage
• R=resistance of the moving coil circuit
• Current through fixed coils, i(f)=I
• Current through the moving coil, i(m)=v/R

Deflecting torque,

• For a DC circuit, the deflecting torque is thus proportional to the power.
• For any circuit with fluctuating torque, the instantaneous torque is proportional to instantaneous power. In this case, due to the inertia of moving parts, the deflection will be proportional to the average power. For sinusoidal alternating quantities, the average power is VI COSθ where
• V = r.m.s. value of voltage,
• I = r.m.s. value of current, and
• θ = phase angle between V and I

Hence an electrodynamic instrument, when connected as shown in the figure, indicates the power, irrespective of the fact it is connected in an AC or DC circuit.

### Ranges:

1. Current circuit: 0.25 A to 100 A with employing current transformers (CTs).
2. Potential circuit: 5V to 750 V without employing potential transformers (PTs).

### Types of Dynamometer Wattmeter:

Dynamometer wattmeters may be divided into two classes:

• Suspended-coil torsion instruments.
• Pivoted-coil, direct indicating instruments.

### 1. Suspended-coil Torsion Wattmeters:

These instruments are used largely as standard wattmeters.

• The moving, or voltage, the coil is suspended from a torsion head by a metallic suspension which serves as a lead to the coil. This coil is situated entirely inside the current or fixed coils and the winding in such that the system is static. Errors due to external magnetic fields are thus avoided.
• The torsion heads carry a scale, and when in use, the moving coil is bought back to the zero position by turning this head; the number of divisions turned through when multiplied by a constant for the instrument gives the power.
• Eddy currents are eliminated as far as possible by winding the current coils of standard wire and by using no metal parts within the region of the magnetic field of the instrument.
• The mutual inductance errors are completely eliminated by making zero position of the coil such that the angle between the planes of moving coil and the fixed coil is 90 degree. i.e. the mutual inductance between the fixed and moving coil is zero.
• The elimination of pivot friction makes possible the construction of extremely sensitive and accurate electrodynamic instruments of this pattern.

### 2. Pivoted-coil Direct-indicating Wattmeters:

These instruments are commonly used as a switchboard or portable instruments.

• In these instruments, the fixed coil is wound in two halves, which are placed in parallel to another at such a distance, that uniform field is obtained. The moving coil is wound of such a size and pivoted centrally so that it does not project outside the field coils at its maximum deflection position.
• The springs are pivoted for controlling the movement of the moving coil, which also serves as currents lead to the moving coil.
• The damping is provided by using the damping vane attached to the moving system and moving in a sector-shaped box.
• The reading is indicated directly by the pointer attached to the moving system and moving over the calibrated scale.
• The eddy current errors, within the region of the magnetic field of the instrument, are minimized by the use of non-metallic parts of high resistivity material.

1)    In dynamometer type wattmeter, the scale of the instrument is uniform (because deflecting torque is proportional to the true power in both DC as well as AC and the instrument is spring controlled.)

2)    High degree of accuracy can be obtained by careful design; hence these are used for calibration purposes.