Measurement of Electrical Quantities: Bridges and Potentiometers, Essays (university) of Electrical Engineering

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AC BRIDGES

Alternating current bridges are most popular, convenient and accurate instruments for measurement of unknown inductance, capacitance and some other related quantities. In its simplest form, ac bridges can be thought of to be derived from the conventional dc Wheatstone bridge. An ac bridge, in its basic form, consists of four arms, an alternating power supply, and a balance detector. SOURCES AND DETECTORS IN AC BRIDGES Selected frequency and discrimination against harmonic frequencies. Vibration galvanometers are most commonly used as tuned detectors in the power frequency and low audio-frequency ranges. Though vibration galvanometers can be designed to work as detectors over the frequency range of 5 Hz to 1000 Hz, they have highest sensitivity when operated for frequencies below 200 Hz. Head phones or audio amplifiers are popularly used as balance detectors in ac bridges at frequencies of 250 Hz and above, up to 3 to 4 kHz. Transistor amplifier with frequency tuning facilities can be very effectively used as balance detectors with ac bridges. With proper tuning, these can be used to operate at a selective band of frequencies with high sensitivity. Such detectors can be designed to operate over a frequency range of 10 Hz to 100 kHz.

When using admittances in place of impedances the product of impedances of one pair of opposite arms must be equal to the product of impedances of the other pair of opposite arms, with the impedances expressed as complex numbers. This will mean, both magnitude and phase angles of the complex numbers must be taken into account. Re-writing the expressions in polar form, impedances can be expressed as where Z represents the magnitude and θ represents the phase angle of the complex impedance. If similar forms are written for all impedances and substituted Thus, for balance we have, two requirements must be met for satisfying balance condition in a bridge In the AC bridge circuit shown in Figure, the supply voltage is 20 V at 500 Hz. Arm AB is 0. 25 mμ pure capacitance; arm BD is 400 Ω pure resistance and arm AC has a 120 Ω resistance in parallel with a 0. 15 mμ capacitor. Find resistance and inductance or capacitance of the arm CD considering it as a series circuit.

MEASUREMENT OF SELF-INDUCTANCE

Maxwell’s Inductance Bridge Unknown quantities can hence be calculated as

Hay’s Bridge

Owen’s Bridge

A Maxwell’s inductance – capacitance bridge is used to measure a unknown inductive impedance. The bridge constants at bridge balance are: Pure resistance arms = 2. 5 kΩ and 50 kΩ. In between these two resistors, the third arm has a capacitor of value 0. 012 μF in series with a resistor of value 235 kΩ. Find the series equivalent of the unknown impedance. The four arms of a bridge are connected as follows: Arm AB: A choke coil L 1 with an equivalent series resistance r 1 Arm BC: A noninductive resistance R 3 Arm CD: A mica capacitor C 4 in series a noninductive resistance R 4 Arm DA: A noninductive resistance R 2 When the bridge is supplied from a source of 450 Hz is given between terminals A and C and the detector is connected between nodes B and D, balance is obtained the following conditions: R 2 = 2400 Ω, R 3 = 600 Ω, C 4 =

1. 3 μF and R 4 = 55. 4 Ω. Series resistance of the capacitor is 0. 5 Ω. Calculate the resistance and inductance of the choke coil.

MEASUREMENT OF CAPACITANCE

De Sauty’s Bridge

MEASUREMENT OF FREQUENCY

Wien’s Bridge

The four arms of a bridge are connected as follows: Arm AB: A capacitor C 1 with an equivalent series resistance r 1 Arm BC: A noninductive resistance R 3 Arm CD: A noninductive resistance R 4 Arm DA: A capacitor C 2 with an equivalent series resistance r 2 in series with a resistance R 2 A supply of 500 Hz is given between terminals A and C and the detector is connected between nodes B and D. At balance, R 2 = 5 Ω, R 3 = 1000 Ω, R 4 = 3000 Ω, C 2 = 0. 3 μF and r 2 = 0. 25 Ω. Calculate the values of C 1 and r 1 , and also dissipation factor of the capacitor. The four arms of a bridge supplied from a sinusoidal source are configured as follows: Arm AB: A resistance of 100 Ω in parallel with a capacitance of 0. 5 μF Arm BC: A 200 Ω noninductive resistance Arm CD: A 800 Ω noninductive resistance Arm DA: A resistance Rx in series with a 1 μF capacitance Determine the value of Rx and the frequency at which the bridge will balance. Supply is given between terminals A and C and the detector is connected between nodes B and D.

A potentiometer is an instrument which is used for measurement of potential difference across a known resistance or between two terminals of a circuit or network of known characteristics. A potentiometer is also used for comparing the emf of two cells. Some important characteristics of potentiometer are the following:  A potentiometer measures the unknown voltage by comparing it with a known voltage source rather than by the actual deflection of the pointer. This ensures a high degree of accuracy.  As a potentiometer measures using null or balance condition, hence no power is required for the measurement.  Determination of voltage using potentiometer is quite independent of the source resistance.

A BASIC DC POTENTIOMETER

Operation CROMPTON’S dc POTENTIOMETER

APPLICATIONS OF dc POTENTIOMETERS Practical uses of dc potentiometers are

• Measurement of current
• Measurement of high voltage
• Measurement of resistance
• Measurement of power
• Calibration of voltmeter
• Calibration of ammeter
• Calibration of wattmeter Measurement of Current by Potentiometer A simple slide wire potentiometer is used for measurement of current in a circuit. The voltage drop across a standard resistor of 0. 1 Ω is balanced at 75 cm. find the magnitude of the current if the standard cell emf of 1. 45 volt is balanced at 50 cm.

Measurement of High Voltage by Potentiometer

Topics to be covered

Measurement of Resistance by Potentiometer Measurement of Power by Potentiometer Calibration of Voltmeter by Potentiometer Calibration of Ammeter by Potentiometer Calibration of Wattmeter by Potentiometer

AC POTENTIOMETERS