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Voltage/Current/Resistance Circuits 57
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4-4 Schematic symbols for incandescent lamp (A), fixed capacitor (B), fixed
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inductor with air core (C), fixed inductor with laminated-iron core (D), chassis ground (E), earth ground (F), signal generator or source of alternating current (G), pair of terminals (H), and specialized component or device (I).
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Suppose you want to build the circuit. You go to an electronics store to get the parts. What values of resistors should you buy How about capacitors What type of transistor will work best Do you need to wind the coils yourself, or can you get ready-made coils Are there test points or other special terminals that should be installed for the benefit of the technicians who might have to repair the amplifier How many watts should the potentiometers be able to handle All these things are indicated in a wiring diagram. You might have seen this kind of diagram in the back of the instruction manual for a hi-fi amplifier, a stereo tuner, or a television set. Wiring diagrams are especially useful when you want to build, modify, or repair an electronic device.
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Most dc circuits can be boiled down to three major components: a voltage source, a set of conductors, and a resistance. This is shown in Fig. 4-5. The voltage or EMF source is E; the current in the conductor is I; the resistance is R. You already know that there is a relationship among these three quantities. If one of them changes, then one or both of the others will change. If you make the resistance smaller, the current will get larger. If you reduce the applied voltage, the current will also decrease. If the current in the circuit increases, the voltage across the resistor will increase. There is a simple arithmetic relationship among these three quantities.
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58 Direct-Current Circuit Basics
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dc circuit. The voltage is E, the current is I, and the resistance is R.
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The interdependence among current, voltage, and resistance in dc circuits is called Ohm s Law, named after the scientist who supposedly first quantified it. Three formulas denote this law: E = IR I = E/R R = E/I You need only remember the first of these formulas in order to derive the others. The easiest way to remember it is to learn the abbreviations E for voltage, I for current, and R for resistance, and then remember that they appear in alphabetical order with the equal sign after the E. Sometimes the three symbols are arranged in the so-called Ohm s Law triangle, shown in Fig. 4-6. To find the value of a quantity, cover it up and read the positions of the others.
4-6 The Ohm s Law
triangle. The voltage is E, the current is I, and the resistance is R. These quantities are expressed in volts, amperes, and ohms, respectively.
Remember that you must use units of volts, amperes, and ohms for the Ohm s Law formulas to yield a meaningful result! If you use, say, volts and microamperes to calculate a resistance, you cannot be sure of the units you ll end up with when you derive the final result. If the initial quantities are given in units other than volts, amperes, and ohms, convert to these units, and then calculate. After that, you can convert the calculated current, voltage, or resistance value to whatever size unit you want. For example, if you get 13,500,000 as a calculated resistance, you might prefer to say that it s 13.5 M .
Current Calculations 59
Current Calculations
The first way to use Ohm s Law is to determine current in dc circuits. In order to find the current, you must know the voltage and the resistance, or be able to deduce them. Refer to the schematic diagram of Fig. 4-7. It consists of a dc voltage source, a voltmeter, some wire, an ammeter, and a calibrated, wide-range potentiometer.
Problem 4-1 Suppose that the dc generator in Fig. 4-7 produces 10 V and the potentiometer is set to a value of 10 . What is the current This is solved by the formula I = E/R. Plug in the values for E and R; they are both 10, because the units are given in volts and ohms. Then I = 10/10 = 1.0 A. Problem 4-2 Imagine that dc generator in Fig. 4-7 produces 100 V and the potentiometer is set to 10 k . What is the current First, convert the resistance to ohms: 10 k = 10,000 . Then plug the values in: I = 100/10,000 = 0.01 A. You might prefer to express this as 10 mA. Problem 4-3 Suppose that dc generator in Fig. 4-7 is set to provide 88.5 V, and the potentiometer is set to 477 M . What is the current This problem involves numbers that aren t exactly round, and one of them is huge. But you can use a calculator. First, change the resistance value to ohms, so you get 477,000,000 . Then plug into the Ohm s Law formula: I = E/R = 88.5 / 477,000,000 = 0.000000186 A. It is more reasonable to express this as 0.186 A or 186 nA.
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