Resistance, Inductance Capacitance Measurements

Resistance, Inductance Capacitance Measurements
Unit-4 Resistance, Inductance and Capacitance Measurements

Introduction Bridge is a simple closed circuit consisting of a network of four resistance arms as shown in figure Bridge circuits are extensively used for measuring component values such as resistance, capacitance, inductance and for other derived circuit parameters directly from component values. The Bridge circuit compares the value of unknown quantity with known quantity, it’s measurement accuracy is very high. Used for performing null measurements on resistances in DC and general impedances on AC. Basic Bridge Circuit

Resistance measurement can be classified into three types
1. Low Resistance 2. Medium Resistance 3. High Resistance

Low Resistance Measurement
Measurement less than 1 ohm comes under this category Low Resistance like i) Armature and series field windings of large machines, ii) Ammeter shunts, iii) Cable length and contacts etc come under this classification

Medium Resistance Measurement
Range between 1 Ohm and 1,00,000 Ohms come under the category of medium resistance measurement Electrical Apparatus come under this resistance range Examples like shunt field windings of machines, Elements of heater, filament of lamp and current limiting resistors etc,

High Resistance Measurements
Resistance greater than 1,00,000 Ohm come under high resistance measurement classification. Examples like insulation resistance of cables and electrical equipments of all types etc

Measurement of low Resistance

Ammeter Voltmeter Method

KELVIN DOUBLE BRIDGE METHOD

WHEATSTONE BRIDGE

CAREY FOSTER BRIDGE METHOD
Slide wire used for finding the difference between the standard resistance ‘S’ and unknown resistance ‘R’. This bridge is a modification of Wheatstone bridge A slide wire of length ‘L’ is included between R and S, the sliding contact is being connected to the galvanometer ‘G’.

LOSS OF CHARGE METHOD In this method, the unknown resistance is connected in parallel with a capacitor C. A voltmeter is connected across the combination Charging and discharging of the capacitance takes place through the resistance The terminal voltage is observed over a considerable period of time during discharge.

A.C.Bridges

Problems

AC Bridges AC Wheatstone bridge determines impedances for Audio and Radio frequencies as shown in figure, it is similar to dc bridge except the bridge arms are impedances. The galvanometer is replaced by a detector, (pair of headphones) for detecting AC. The bridge is balanced when Z1 / Z3 = Z2 / Z4 where Z1 , Z2 ,Z3 ,Z4 are impedances of the arms. Balanced condition is achieved by adjusting both the magnitude and phase angles of impendence arms. AC Wheatstone Bridge

Measurement of Inductance
Inductance Comparison Bridge Measurement of Inductance Figure shows an inductance comparison bridge, the values of unknown inductance Lx and its internal resistance Rx are obtained by comparing with standard values L3 and R3. The equation for balanced condition Z1 Zx= Z2 Z3 Induction balance condition is Lx = L3 R2 / R1 Resistive balance condition is Rx = R2 R3 / R1 where R2 - chosen as inductive balance control R3 – Resistance balance control Inductance Comparison Bridge

Measurement of Inductance
Inductance Comparison Bridge Balance condition is obtained by varying L3 or R3 If Q of unknown reactance is greater than standard Q, then a variable resistance is placed in series with unknown reactance to obtain balance. If unknown inductance has high Q value, then it is varied by using resistance ratio when standard inductor is not available. The inductance of bridge can be measured by using Inductance Comparison Bridge Maxwell’s Bridge Anderson Bridge Prev. Next

Inductance Comparison Bridge
Maxwell’s Bridge It measures an unknown inductance in terms of known capacitance. Standard arm used in the circuit is to achieve compactness and easy shielding. One arm has a resistance R1 in parallel with capacitor C1 (loss less component), balanced equation can be written using admittance instead of impedance. Bridge balanced condition Z1 Zx= Z2 Z3 Maxwell’s Bridge 1 Prev. Next

Maxwell’s Bridge Where Z1=R1 is in parallel with C1 i.e., Y1=1/Z1 Maxwell’s Bridge

Maxwell’s Bridge By Equating real and imaginary terms, It is limited to measure only low Q values (1-10), measurement is independent of excitation frequency. 5 Maxwell’s Bridge

Maxwell’s Bridge Using fixed capacitor, has the disadvantage of interaction between the resistance and reactance balances. Inorder to avoid interaction and to obtain reactance balance, capacitances are varied instead of Resistance (R2) and Reactance (R3). This bridge is mostly used for measuring inductances because comparison with capacitor is more ideal than with other inductance. Maxwell’s Bridge Prev. Next

Anderson Bridge This is modified Maxwell’s bridge used for measuring self-inductance interms of standard capacitor. One arm of bridge consists of an unknown inductor L1 in series with known resistance R1. C-Standard capacitor with r, R2 ,R3 and R4 (non-inductive known resistances) Bridge balance equations are i1=i3 ,i2=i4+iC , V2=i2R2 , V3=i2R3 Anderson Bridge Next Prev

Measurement of Capacitance
Capacitance Comparison Bridge The arms R1 , R2 are Resistive. Capacitor C3 is in series with R3.Cx is the unknown capacitor, Rx is the small leakage resistance of capacitor. The value is obtained by comparing an unknown capacitor with standard capacitor. Hence Z1 =R1 , Z2 =R2 Bridge balance condition Z1Zx= Z2Z3 Capacitance Comparison Bridge Next

Capacitance Comparison Bridge 3 Two complex quantities are equal when their real and imaginary terms are equal. As R3 does not appear in the expression for Cx , as a variable element it is an obvious choice to eliminate any interaction between the two balance controls. 4 Capacitance Comparison Bridge Next Prev.

Capacitance Comparison Bridge The capacitance of bridge can be measured by using Schering Bridge Wheatstone Bridge Wien’s Bridge

Capacitance Comparison Bridge
Schering’s Bridge It is most important bridge , extensively used for the precision measurement of capacitors, particularly for testing small capacitors at low voltages with high precision. Capacitor C3 used is of high quality mica capacitor(low loss)for insulation measurement. Bridge balanced condition Z1 Zx= Z2 Z3 Zx=Z2Z3/Z1 Schering’s Bridge

Schering’s Bridge By equating real and imaginary parts, we get Schering’s Bridge 5

Schering’s Bridge The dial of capacitor C1 is calibrated directly to give dissipation factor(D) at a particular frequency. D=Rx/Xx=ωCxRx where D-quality of the capacitor(or) reciprocal of quality factor(1/Q) (or) dissipation factor. A high voltage is dropped across C3 and Cx and a little across R1 and R2 ,because the reactance of capacitors C3 and Cx are higher than resistances R1 and R2. If the junction of R1 and R2 is grounded, detector is effectively at ground potential, reducing stray-capacitance effect which makes the bridge more stable. Schering’s Bridge

Wheatstone Bridge This is the most accurate method for measuring resistances The source and switch are connected to points A and B, current indicating meter and galvanometer are connected to points C and D as shown in circuit. Galvanometer: It is a sensitive microammeter, with a zero center scale. If there is no current through the meter, the galvanometer pointer rests to 0. Current in one direction makes the pointer to deflect on one side, and in opposite direction to the other side. Wheatstone Bridge

Capacitance Comparison Bridge Capacitance Comparison Bridge
Wheatstone Bridge When SW1 is closed: Current divides at point A i.e., I1 and I2. The bridge is balanced when the potential difference across points C and D are equal(no current flows through the galvanometer) Bridge balance equation I1R1 =I2R2 The following conditions satisfies, the galvanometer current to be zero I1=I3=E/(R1+R3) I2=I4=E/(R2+R4) 1 2 3

Wheatstone Bridge Substituting (2) and (3) in (1) (E*R1 )/(R1+R3) = (E*R2)/(R2+R4) R1*(R2+R4) = (R1+R3)*R2 (R1*R2)+(R1*R4 )=(R1*R2)+(R3*R2) R4 =(R2*R3)/R1 (equation for the bridge to be balanced) Practically Wheatstone bridge is given as Rx =(R2*R3)/R1 Wheatstone Bridge Prev. Next

Wheatstone Bridge Sensitivity of a Wheatstone Bridge Current flows through the galvanometer when the bridge is in an unbalanced condition, making the pointer to deflect. Deflection is sensitivity of galvanometer. Sensitivity is given as deflection per unit current. Deflection may be expressed in linear or angular units of measure, sensitivity S is expressed in units of S=mm/µA or degree/µA or radians/µA The total deflection D is D=S*I, where S-Sensitivity I-Current in microamperes

Wheatstone Bridge Unbalanced Wheatstone Bridge Thevenin’s Theorem is applied to the circuit to determine the amount of deflection. Thevenin's equivalent voltage: Determined by disconnecting galvanometer from the bridge circuit, and by open circuiting voltage between the terminals a and b as shown in figure Voltage determined at point ‘a’ is Ea=(E*R3) / (R1 +R3) at point ‘b’, Eb = (E*R4) / (R2 +R4) Voltage between a and b is difference between Ea and Eb (Thevenin’s equivalent voltage) Unbalanced Wheatstone Bridge

Wheatstone Bridge Unbalanced Wheatstone Bridge Unbalanced Wheatstone Bridge Thevenin’s equivalent resistance: Determined by replacing voltage source(E) with its internal impedance (or) short circuited and calculating internal resistance by looking into terminals a and b. Internal resistance is assumed to be very low (0 Ω). Thevenin’s Resistance

Wheatstone Bridge Unbalanced Wheatstone Bridge As shown in the figure R1//R3 in series with R2//R4 it can be written as R1//R3 + R2//R4 Thevenin’s equivalent circuit for the bridge, from terminals a and b is shown in Thevenin’s Equivalent figure The Unbalanced wheat stone Bridge and Thevenin’s equivalent as shown in figure experience same deflection at the output of bridge. Thevenin’s Resistance Thevenin’s Equivalent

Wheatstone Bridge Unbalanced Wheatstone Bridge The resistance between a and b has only galvanometer resistance (Rg). The deflection current in galvanometer is Ig=Eth/(Rth + Rg) Thevenin’s Equivalent Prev.

Wien’s Bridge It has a series RC combination in one arm and parallel combination in adjoining arm. It is designed to measure frequency and unknown capacitor with great accuracy. The impedance of one arm is Admittance of parallel arm is According to bridge balance equation, Wien’s Bridge

Wien’s Bridge By equating real and imaginary parts, we get (4) (5) Wien’s Bridge

Wien’s Bridge Equation (4) determines the required resistance ratio R2 /R4 and equation (5) determines the frequency of applied voltage, if these equations are satisfied then the bridge is said to be balanced. The circuit components of Wien bridge are chosen such that R1 = R3 = R and C1= C3 = C Wien Bridge is used in harmonic distortion analyzer, as a Notch filter and as a frequency determining element in audio and radio frequency oscillators 0.5%-1% accuracy is obtained by using this bridge. It is difficult to balance the bridge unless the waveform of applied voltage is purely sinusoidal. Wien’s Bridge

Errors and Precautions in Using Bridges
Precautions to obtain accurate readings: The leads should be laid out in such a way that no loops or long lengths enclosing magnetic flux are produced with stray inductance errors. Measuring Inductance(Large ‘L’): In this self-capacitance of the leads is more important than inductance, so they should be spaced far apart. Measuring Capacitance: It is important to keep the lead capacitance as low as possible, the leads should not be too close and should me made of fine wire. Precise Inductive and Capacitance Measurements: Leads are enclosed in metal tubes to shield them from electro magnetic action, and are designed completely to shield the bridge.

Circuit Diagram of Q-meter
Q-meter is an instrument used to measure total efficiency of coils and capacitors for RF applications. Q meter is based on the principle of series resonance, the voltage drop across coil or capacitor is Q times the applied voltage Q is the ratio of reactance to resistance. At resonance XL=XC and EL=IXL, EC=IXC ,E=IR where E-applied voltage EC –Capacitor voltage EL –Inductive voltage XL – Inductive Reactance XC –capacitive reactance R-coil resistance I- circuit current Circuit Diagram of Q-meter

Circuit Diagram of Q-meter
Therefore Q=(XL/R)=(XC/R)=(EC/E) In the above equation if E is constant ,the voltage across the capacitor is measured by voltmeter calibrated to read directly in terms of Q. The oscillator with frequency range from 50 KHz to 50 MHz ,supplies current to resistance Rsh having a value of 0.02 Ω(almost no resistance),represents a low voltage source ‘e’ with small internal resistance. The voltage across Rsh is measured with thermocouple meter, voltage across capacitor is measured with electronic voltmeter corresponding to Ec , and the value is calibrated directly to read Q. Circuit Diagram of Q-meter

Q Meter Circuit is tuned to resonance by varying C until voltmeter reads maximum value. Resonance output voltage E, corresponding to EC , is E=Q*e i.e., Q=E/e where e-electronic voltmeter Inductance of coil is determined by connecting to the test terminals of instrument, circuit resonance occurs either by varying capacitance or oscillator frequency. “Multiply Q by” switch is used to obtain actual Q value. Inductance of coil is calculated from known values of coil frequency and resonating capacitor (C). Diagram of Q-meter 6

Q Meter Because of the losses due to resonating capacitor, voltmeter and resistors in measuring circuit, the value of Q decreases(actual value of Q is greater). Difference between actual and indicated Q is negligible , except when the resistance of coil is small compared to inserted resistance Rsh. Diagram of Q-meter

Q Meter Factors that May Cause Error
At high frequencies electronic voltmeter suffers from losses due to transit time effect. As shown in figure, Rsh introduces an additional resistance in tank circuit. To make Qobs value close to Qact ,Rsh value is made as small as possible. Rsh value introduces an error negligibly from Ω. Effect of Rsh on Q

(a) Measurement of Stray Capacitance
Q Meter Factors that May Cause Error Another source of error is the distributed capacitance or self capacitance of measuring circuit. These capacitances modifies the actual Q and inductance of the coil. At resonant frequency the self capacitance and inductance of the coil are equal, circuit impedance is purely resistive(can be used to measure distributed capacitance) Methods For Determining Stray Capacitance (or) Distributed Capacitance First method to determine distributed capacitance(Cs) is by plotting graph of 1/f2 against C in pico farads Value of C for resonance is noted by varying the frequency of oscillator in Q meter. Effect of Rsh on Q (a) Measurement of Stray Capacitance

(a) Measurement of Stray Capacitance
Q Meter Factors that May Cause Error The straight line intercepting the X-axis gives the value of Cs. The value of unknown inductance is determined by If 1/f2=0,then C=-Cs . (a) Measurement of Stray Capacitance Effect of Rsh on Q

(b) Measurement of Stray Capacitance
Q Meter Factors that May Cause Error Methods For Determining Stray Capacitance (or) Distributed Capacitance Second method for determining distributed capacitance is making two measurements at different frequencies. The capacitor (C) of Q meter is calibrated to indicate the capacitance value. The test coil is connected to Q meter terminals, as shown in figure (b) The circuit is resonated by varying the oscillator frequency, it is found to be f1 Hz and the capacitor value as C1 (b) Measurement of Stray Capacitance

Q Meter Factors that May Cause Error The oscillator frequency of Q meter is increased to twice the original frequency f2 =2f1 and capacitor is varied until resonance occurs at C2 Resonant frequency of an LC circuit is given by For initial resonance condition, the total capacitance of circuit is (C1+Cs) and resonant frequency equals After varying the oscillator and tuning capacitor for the new value of resonance (f2), the capacitance is (C2+Cs), therefore (b) Measurement of Stray Capacitance 7 8

Q Meter Factors that May Cause Error But f2=2f1 By substituting equations (7) and (8) in (9) we get C1=4C2+3Cs 3Cs=C1-4C2 Cs=(C1-4C2)/3 By using equation (10) distributed capacitance is calculated 9 10 (b) Measurement of Stray Capacitance

(a) Series Substitution Method
Q Meter Impedance Measurement Using Q Meter An unknown impedance is measured either by series (small) or shunt(large) In Q meter method of measurement of Z, the unknown impedance Zx is determined by determining Rx and Lx Series Substitution Method: When the unknown impedance is shorted the tuned circuit is adjusted for resonance at the oscillator frequency, the values of Q and C are noted. When the unknown impedance is connected, the capacitor is varied for resonance, new values of Q΄and C΄are noted. (a) Series Substitution Method

(a) Series Substitution Method
Q Meter Impedance Measurement Using Q Meter Series Substitution Method: (a) Series Substitution Method In the above equation jXx is an imaginary term, Negative value indicates capacitive reactance and Positive value indicates inductive reactance.

(b) Shunt Substitution Method
Q Meter Impedance Measurement Using Q Meter Shunt Substitution Method(for Large impedance) If Zx>XL ,the unknown impedance is shunted across the coil and capacitor, as shown in figure. Yx –shunt admittance of unknown impedance, it has two shunt elements conductance Gx , susceptance Bx. At oscillator frequency the values of Q and C are noted, after connecting Yx the capacitor is tuned again for resonance and the new values of Q΄and C΄are given as (b) Shunt Substitution Method

Q Meter Impedance Measurement Using Q Meter
The accuracy for the method of substitution is high. Error is mainly because C΄cannot be accurately determined due to additional resistance, the resonance curve may be flat. The stray inductance with tuning circuit causes errors at VHF. Substitution method is used for measuring the losses of coil. It cannot measure the losses of an air-dielectric capacitor, because they are too small to be detected by this method.

(a) Series Substitution Method of Measurement
Q Meter Measurement of Characteristic Impedance (Z0) of a Transmission Line Using Q Meter Series Substitution Method (Low impedance ): A transmission line or cable is tuned for series resonance. Series substitution is used to determine Z0 = R0 + jX0 (for transmission line)x Reactance/unit length of the line is total reactance divided by length (l). Series resonance occurs when the line is short circuited, line length is an even multiple of λ/4 and when open circuited an odd multiple of λ/4 . (a) Series Substitution Method of Measurement

(b) Shunt Substitution Method of Measurement
Q Meter Measurement of Characteristic Impedance (Z0) of a Transmission Line Using Q Meter Shunt Substitution Method( High impedance): Parallel resonance occurs when the line is short circuited and length of line is odd multiple of λ/4, or open circuited it is an even multiple of λ/4. (b) Shunt Substitution Method of Measurement

(a) Susceptance Method
Q Meter Measurement of Q by Susceptance Method The coil is connected in series with low loss variable capacitor, as shown in figure (a). The circuit is tuned for resonance to the oscillator frequency, by varying the variable capacitor C to value Cr. The capacitor is detuned to value Cb on low capacitance side of resonance ,the meter reading falls to 70.7% of the resonant voltage. Next, the capacitor is set on the higher capacitance side of resonance to value C, here the voltmeter deflection again drops to 70.7% of the resonant voltage, as shown in Fig(b). (a) Susceptance Method (b) Response Curve

Q Meter Measurement of Q by Susceptance Method
The points Ca, Cb, and Cr are closer together when coil Q is high (sharp tuning) and far apart when Q is low (broad tuning). The value of Q is determined as follows. (b) Response Curve

Q Meter Measurement of Q by Susceptance Method
where Ca and Cb are capacitance values at the half power point and Cr is the value of the capacitance at resonance. The frequency of the signal generator is kept at a suitable value and the output across capacitor is measured by an electronic voltmeter. This method requires less expensive components than Q meter.

Applications of Bridges
Bridges measure dc and ac resistance of various types of wire. Example: Resistance of motor windings, Transformers, Relay Coils, Telephone Companies and others to locate cable faults. Wien’s Bridge is used in Harmonic distortion analyzer, as a Notch filter and as a frequency determining element in audio and radio frequency oscillators. Relay coil Transformer

Limitations of Bridges
For low resistance measurement, the resistance of leads and contacts introduces an error. For high resistance measurements, the resistance of bridge becomes so large that the galvanometer is insensitive to imbalance. Change occurs in resistance of bridge arms due to heating effect of current. Rise in temperature causes change in value of resistance, excessive current may cause a permanent change in value. Using fixed capacitor in Maxwell’s Bridge, has the disadvantage of interaction between the resistance and reactance balances.

Summary Bridge is a simple closed circuit consisting of a network of four resistance arms. Bridge circuits are used for measuring parameters such as resistance, capacitance, inductance AC Wheatstone bridge determines impedances for Audio and Radio frequencies, it is similar to dc bridge except the bridge arms are impedances. Maxwell’s bridge measures an unknown inductance in terms of known capacitance. Schering’s Bridge is used for the precision measurement of capacitors, for testing small capacitors at low voltages with high precision. Wheatstone bridge is accurate method for measuring Resistances. The source and switch are connected to points A and B, current indicating meter and galvanometer are connected to points C and D in the circuit.

Summary Wien’s bridge has a series RC combination in one arm and parallel combination in adjoining arm. It is designed to measure frequency and unknown capacitor with great accuracy. Wien’s Bridge is used in Harmonic distortion analyzer, as a Notch filter and as a frequency determining element in audio and radio frequency oscillators. Q-meter is an instrument used to measure total efficiency of coils and capacitors for RF applications.

WAGNERS EARTH (GROUND) CONNECTION
When performing measurements at high frequency, stray capacitances between the various bridge elements and ground, and between the bridge arms themselves, become significant. This introduces an error in the measurement, when small values of capacitance and large values of inductance are measured. An effective method of controlling these capacitances, is to enclose the elements by a shield and to ground the shield. This does not eliminate the capacitance, but makes it constant in value. Another effective and popular method of eliminating these stray capacitances and the capacitances between the bridge arms is to use a Wagner's ground connection. Figure shows a circuit of a capacitance bridge. C1 and C2 are the stray capacitances. In Wagner*s ground connection, another arm, consisting of Rw and Cw forming a potential divider, is used. The junction of Rw and Cw is grounded and is called Wagner's ground connection. The procedure for adjustment is as follows. The detector is connected to point 1 and R1 is adjusted for null or minimum sound in the headphones. The switch S is then connected to point 2, which connects the detector to the Wagner ground point. Resistor Rw is now adjusted for minimum sound. When the switch S is connected to point 1, again there will be some imbalance.

Resistors R1 and R3 are then adjusted for minimum sound and this procedure is repeated until a null is obtained on both switch positions 1 and 2. This is the ground potential. Stray capacitances C1 and C2 are then effectively short-circuited and have no effect on the normal bridge balance. The capacitances from point C to D to ground are also eliminated by the addition of Wagner's ground connection, since the current through these capacitors enters Wagner's ground connection. The addition of the Wagner ground connection does not affect the balance conditions, since the procedure for measurement remains unaltered.

Resistance, Inductance Capacitance Measurements

Similar presentations

Presentation on theme: "Resistance, Inductance Capacitance Measurements"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Resistance, Inductance Capacitance Measurements

Similar presentations

Presentation on theme: "Resistance, Inductance Capacitance Measurements"— Presentation transcript:

Similar presentations

About project

Feedback