**Measurement of Low, Medium & High Resistances**which will cover the topics such as

**Classification of Resistance, to Measure Low Resistances are Kelvin Bridge Method, Kelvin-Double Bridge Method, to Measure Medium Resistances such as Ammeter-Volt Meter Method,**

**Ohmmeter Method,**

**Wheat Stone Bridge Method, to measure high resistances**

**Direct Deflection method, Loss of Charge method & Megha ohm bridge method.**

### Classification of Resistance

**Low Resistance**is the range of**'0.1Ω to 1Ω'**.**Medium Resistance**is the range of**1Ω to few Megha ohm**.**High resistance**is**.1MΩ to**the**higher**range.

**Methods For Measurement of Low Resistances**

- Kelvin Bridge Method
- Kelvin Double Bridge
- Ammeter – voltmeter method

**Methods For Measurement of Medium Resistances**

- Ammeter–Voltmeter method
- Wheat stone bridge method
- Ohmmeter method

**Methods For Measurement of High Resistances**

- Direct Deflection methods
- Loss of Charge methods
- Megha ohm bridge methods

**Measurement of Low Resistances**

When the resistance to be measured is of the order of magnitude of bridge contact and lead resistance, a modified form of Wheatstone’s bridge, the Kelvins Bridge theory is employed.

**Kelvin Bridge Method **

**Kelvins Bridge theory** is a **modification of Wheatstone’s bridge** and is used to measure values of resistance below 1 Ω. In low resistance measurement, the resistance of the leads connecting the unknown resistance to the terminal of the bridge circuit may affect the measurement.

### and the usual balance equations for the bridge give the relationship**Kelvin Double Bridge Method: **

- Kelvin’s Double bridge is a modification of Kelvins Bridge theory
**’s**bridge and always used in the measurement of low resistance. - It uses two sets of ratio arms and the four terminal resistances for the low resistance consider the ckt.
- The first set of ratio P and Q.
- The second set of ratio arms are p and q is used to connected to the galvanometer to
**a pt d**. - At an Approx. potential between points m and n to eliminate the effects of connecting lead of resistance r between the known
**std. resistance ‘s’**and**unknown resistance R**. - The ratio
**P/Q**is made**equal to p/q**. under balanced condition there is no current flowing through galvanometer which means voltage drop between a and b,**E**to the_{ab}equal

voltage drop between a and c,**E**_{amd}.

**I _{1}P=I_{2} R**

**I**

_{1}=I_{3}=E/P+Q**I**

_{2}=I_{4}=E/R+S**E=emf of the battery**

If three of the resistances are known then fourth may be determined by formula…

**R=S*P/Q**

Where **R** is the** unknown resistance,** **S** is called the **standard arm resistor** and **P and Q are called the ratio arms.**

**Methods For Measurement of Medium Resistances**

- Ammeter–Voltmeter method
- Wheat stone bridge method
- Ohmmeter method

**Ammeter-Volt Meter Methods**

- We measured the current and the voltage across a variable resistance using the voltmeter-ammeter method, in this method we used two galvanometers with specified range discussed, later on, three-decade boxed the first one is used as the variable resistance Rx, the second and the third are the shunt and series resistances for the ammeter and the voltmeter.
- We must know how to convert the galvanometer into a voltmeter or an ammeter. To convert a
**PMMC**into a voltmeter we connect a series resistance with it, the value of this resistance changes according to the value of**R**._{x}

There are **two possible connections** for the measurement of Medium Resistance using Ammeter Voltmeter Method as shown in the figure below: In both the cases, the reading of Voltmeter and Ammeter is taken.

**If the Voltmeter reading is V and Ammeter reading is I then the measured Resistance will be**

**R _{m} = V/I**

- This measured Resistance Rm will be the true value of the Resistance if and only if the Resistance of Ammeter is zero and that of Voltmeter is infinite.
- But actually, this is not possible to achieve zero resistance Ammeter and infinite Resistance Voltmeter. Therefore the measured value of resistance Rm will deviate from the true value R (Say).

**Case 1: **

**The voltmeter is measuring the Voltage drop across the Ammeter as well as the resistor.**

It is clear from the **figure (1)** that Voltmeter is measuring the Voltage drop across the Ammeter as well as the resistor.

So **V = V _{a} + V_{r}**

Let current measured by Ammeter = I

Therefore, measured Resistance **R _{m} = V/I**

So, **R _{m} = (V_{a}+V_{r}) / I =(IR_{a}+IR) / I = R_{a}+R**

Therefore, the measured Resistance is the sum of Resistance of Ammeter and true Resistance. Therefore measured value will only represent true value if **Ammeter Resistance R _{a} is Zero**.

True value of Resistance** R = R _{m}–R_{a}= R_{m}(1-R_{a}/R_{m})**

Relative Error =** (R _{m}-R)/R = R_{a}/R**

**Note: **Relative Error will be less if the true value of Resistance to be measured is high as compared to the internal Resistance of Ammeter.

**Case 2:**

** The voltmeter is connected in which Voltmeter is connected toward Resistance R whose value is to be measured, Here Ammeter will read the current flowing through the Voltmeter and Resistance R.**

Therefore current measured by Ammeter I_{a} = I_{v}+I_{r}

So, I_{a} = I_{v}+I_{r}

**Measured Resistance**

**R _{m} = V/I_{a }= V/(V/Rv+V/R) = RvR/(R+Rv) = R/(1+R/Rv) **

Therefore,** true value of Resistance R** **= R _{m}R_{v}/(R_{v}-R_{m})**

**= R _{m}(1-R_{m}/R_{v})**

Therefore, **the true value of Resistanc**e will only be equal to measured value if the value of Voltmeter Resistance Rv is infinite.

If we assume that the value of **Voltmeter Resistance R _{v} **is large as compared to the Resistance to be measured R, then

**R**

_{v}>>>R_{m}**So, True value R = R _{m}(1+R_{m}/R_{v})**

Thus from the above equation, it is clear that the measured value of Resistance is smaller than the true value.

**Relative Error = (R _{m}-R)/R**

** = -R/Rv**

Therefore, it is clear from the expression of Relative Error that, error in measurement will be low if the value of Resistance under measurement is very less as compared to the internal Resistance of Voltmeter.

**Wheat Stone Bridge Method**

- The Wheatstone bridge is a circuit used to compare an unknown resistance with a known resistance.
- The bridge is commonly used in control circuits. For instance, a temperature sensor in an oven often consists of a resistor with a resistance that increases with temperature.
- This temperature-dependent resistor is compared with a control resistor (outside the oven) to control a heater and maintain a set temperature.

Since **V _{AB} = 0**, the voltage drop from C to A must equal the voltage drop from C to B,

**V**. Likewise, we must have

_{CA}= V_{CB}**V**. So we can write,

_{AD}= V_{BD}Thus, the **unknown resistance** **R _{x} **can be computed from the known resistance

**R**and the known ratio.Notice that the computed

_{k}**R**does not depend on the voltage

_{x}**V**; hence,

_{o}**V**does not have to be very stable or well-known.Another advantage of the Wheatstone bridge is that, because it uses a

_{o}**, the galvanometer does not have to be calibrated.**

*null measurement*, (V_{AB}= 0)**Temperature dependence of resistivity**

For this part, the unknown R_{x} is a copper wire coilAs a measure of how sensitive the resistivity is to temperature changes, we can compute the fractional change in the resistivity divided by the change in temperature

**Ohmmeter Method**

- The ohmmeter is an electronic instrument which is widely used to check a complete circuit or to measure the resistance of a circuit element.
- Micro-Ohmmeter, Mega Ohmmeter, and Milli- Ohmmeters are used to measure resistance in different applications of electrical testing.

**Series Ohm-Meter**

In a series type Ohmmeter, the R_{1} is the current limiting resistor, the R_{x} is the unknown resistor, the R_{2} is the zero adjust resistor, the R_{m} is the internal resistance, E is the internal battery voltage, and A and B are the output terminals of the Ohmmeter_{.}

In a series type Ohmmeter, the **R _{1} is the current limiting resistor,** the

**R**, the

_{x}is the unknown resistor**R**adjust resistor, the

_{2}is the zero**R**, E is the internal battery voltage, and A and B are the output terminals of the Ohmmeter.

_{m}is the internal resistance**Shunt Type Ohmmeter**

Shunt type Ohmmeter is used to measure small values of resistance.In this type of Ohmmeter, the movement mechanism is connected parallel to the unknown resistance R_{x}.When the** A and B terminals are closed**, then the unknown resistor **R _{x}** is

**short-circuited**, the

**needle reads zero**because full current flows through the resistor

**R**through the meter. Therefore, zero current reading is marked as

_{x}, and I=0**0 Ohms**.

When the **A and B terminals are opened**, then the unknown resistor **R _{x} **is

**open circuited**, no current flows through the

**R**and full-scale current flows through the meter as the resistor

_{x}**R**is adjusted. So, maximum current reading is marked

_{1}**∞ Ohms.**

**Methods For Measurement of High Resistances**

- Direct Deflection methods
- Loss of Charge methods
- Megha ohm bridge methods

**Megohm Bridge Method**

- We have seen many methods to find low and medium resistances here we discuss
**methods for high resistance measurement.**So now I will explain**Megohm bridge method**. - In the given figure below it shows a very high resistance R with its two main terminals A and B, and a guard terminal, which is put on the insulation.
- This high resistance R is between main terminals A and B and the leakage resistances
**RAG and RBG**between the main terminals A and B of from a "**Three-terminal resistance**".

- The
**operation of a Mega ohm bridge**can be explianed as it is a self-contained**Mega ohm bridge**which includes power supplies, bridge a member, amplifiers, and indicating instrument. **It has a range from 0.1 MΩ to 10⁶ MΩ**. The**accuracy is within 3%**for the lower part of the range to possible**10% above 10,000 MΩ.**

**Loss of Charge Method**

- In the circuit C is a capacitor of known capacitance, V is electrostatic volt-meter, R1 is the total leakage resistance of the capacitor and volt-meter and R is the resistance to be measured.
- In this method, the capacitor is first charged by means of a battery to some suitable voltage by putting switch S on stud 1 and then allowed to discharge through the resistances R and R1 by throwing switch S to stud 2.
- The time taken t for the potential difference to fall from V1 to V2 during discharge is observed by a stopwatch. The equivalent resistance of R1 and R is given as

**R’ = t/(C loge V _{1}/V_{2} ) **

- From the above expression the value of R’ can be determined. The test is then repeated with unknown resistance R disconnected, the capacitor being discharged through R1 can also be determined. Knowing the value of R’ and R1 the value of unknown resistance can be determined from the relation

**1/R = 1/R-1/R _{1}**

- While measuring insulation resistance of a cable or a capacitor the test need not be repeated. In this case, C will be the capacitance of the cable (or capacitor) under test, which must be known (may be determined by any method if not known) and R1 will be the insulation resistance to be measured. NO external resistance is to be inserted in the circuit. The value of R1 then can be obtained directly from the expression.

**R = t/(C log V _{2}/V_{1} **

This method of measurement is associated with serious difficulties and error such as

- Leakage and absorption effects
- Effect of time electrification and
- Effect of temperature upon insulation resistance.

### Direct Deflection Method

- The figure shows the measurement of
**high resistance using direct deflection method.** - For measurement of high resistance such as insulation resistance of cables, a sensitive galvanometer of d’Arsonval type is used in place of the microammeter.
- In fact, many sensitive type of galvanometers can detect currents from
**0.1-1nA**.therefore, with an applied voltage of 1kV, resistance as high as**10**to^{12}**10*10**can be measured.^{12O} - The first figure shows the direct deflection method for measurement of high resistance having the metallic sheath.
- The galvanometer G shows the current between the conductor and the metallic sheath.
- The leakage current is carried by the guard wire wound on the insulation and therefore does not flow through the galvanometer.

If you are preparing for GATE and ESE, avail Online Classroom Program to get unlimited access to all the live structured courses and mock tests from the following link :

**ESE and GATE ECE Online Classroom Program (24+ Live classes and 150+ mock tests)****ESE and GATE EE Online Classroom Program (24+ Live classes and 193+ mock tests)**

Thank you,

**Download BYJU'S Exam Prep, Best gate exam app**

**for Preparation**

## Comments

write a comment