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Unknown resistance FIGURE 1944 Ohmmeter
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5 Wheatstone Bridge A Wheatstone bridge circuit (shown in Fig 1945) is
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normally used for the comparison and measurement of resistances in the range of to 1 M The cornerstone of the bridge consists of the four resistances (R1, 1 R2, R3, Rx), which are arranged in a diamond shape An unknown resistance Rx is compared with others of known values, ie, R1 and R2, which have xed values, and R3 which is variable R3 is varied until zero de ection is obtained on the galvanometer G No current then ows through the meter, VA VB, and the bridge is balanced, ie; R1 Rx or Rx R2 R3 R1 ( ) R2 R3
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The last equation gives Rx in terms of the other three known resistors in the bridge
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6 Cathodic-Ray Oscilloscope The cathodic-ray oscilloscope (cro) is a useful
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and versatile device characterized by high input impedence and wide frequency range It is used in the observation of waveforms and for the measurements of voltage, current, frequency, phase and periodic time
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A R1 R3 G R2 B Rx
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FIGURE 1945 Wheatstone bridge
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The heart of any oscilloscope is the cathode-ray tube which is shown schematically in Fig 1946 Electrons are released from the hot cathode and accelerated toward the screen by the use of a positively charged anode An appropriate grid arrangement then governs the focus of the electron beam on the screen The exact position of the spot on the screen is controlled by the use of the horizontal and vertical de ection plates A voltage applied on one set of plates produces the x de ection, while a voltage on the other set produces the y de ection Thus, with appropriate voltages on the two sets of plates, the electron beam may be made to fall on any particular spot on the screen of the tube The screen is coated with a phosphorescent material, which emits light when struck by the electron beam For example, a sinusoidal waveform is displaced on a cro screen for alternating voltage measurements (see Fig 1947) If the time / cm switch is on, say 5 ms / cm, then the periodic time t of the sine wave is 5 ms / cm 4 cm, ie 20 ms or 002 s Then frequency
Vertical deflection plates Cathode Anode
Horizontal deflection plates
Electron beam Y input
Fluorescent screen
Sawtooth sweep or X input
FIGURE 1946 Schematic diagram of a cathode-ray tube
Peak-to-peak value
1 5 2 05 02 10 20 V/cm 30 40 50 5 ms 100 s 50 ms s/cm 2s
Periodic time
FIGURE 1947 The cro screen measurements (example)
CHAPTER NINETEEN
1 002
50 Hz
If the volts / cm switch is on, say 20 volts / cm, then the amplitude or peak volume of the sine wave shown is 20 volts / cm 2 cm 40 V Therefore the rms voltage peak voltage 2 40 2 2828 (V)
Double beam oscilloscopes are useful whenever two signals are to be compared simultaneously In adjustment and use of the cro, reasonable skill is needed However, the cro s greatest advantage is in observing the shape of a waveform a feature not possessed by other measuring instruments
7 Q-Meter The simpli ed circuit of a Q-meter, used for measuring Q-factor, is shown in Fig 1948 The Q-factor for a series L-C-R circuit is the voltage magni cation at resonance, ie:
Q-factor
voltage across capacitor supply voltage
Vc V
Current from a variable frequency oscillator owing through a very low resistance R0 develops a variable frequency voltage, VR0, which is applied to a series L-R-C circuit The frequency is then varied until resonance causes voltage Vc to reach a maximum value At resonance VR0 and Vc are noted, then: Q-factor Vc VR0 Vc i R0
In practice, VR0 is maintained constant Then, if a variable capacitor C is used and LC), C can be adjusted to give the oscillator is set to a given frequency ( 1 / 2 resonance In this way, inductance L can be calculated from the following relation since:
Variable frequency oscillator
R0 VR0 C
Coil under test
Electronic voltmeter
FIGURE 1948 Q-meter circuit
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L R
8 Wattmeter A wattmeter is an instrument for measuring electrical power in a
circuit The product of potential difference V and current i gives power P in an electrical circuit Fig 1949 shows typical connections of a wattmeter used for measuring power supplied to a load The instrument has measuring power supplied to a load The instrument has two coils: a) a current coil, which is connected in series with the load, like an ammeter, and b) a voltage coil, which is connected in parallel with the load, like a voltmeter V2 As electrical power P V i i2 R (watts) the electrical energy (power R time) is expressed in watt seconds ( jouls) If the power is measured in kilowatts and the time in hours, then the unit of energy is kilowatt-hours The electricity meter in the home records the number of kilowatt-hours used
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