Physics
Voltage Sources in Series
When voltage sources are connected in series, their voltages add up to create a total voltage. If the sources have the same polarity, their voltages are added directly. If the sources have opposite polarities, their voltages are subtracted. The total voltage across the series combination is the algebraic sum of the individual voltages.
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2 Key excerpts on "Voltage Sources in Series"
- Frank R. Spellman(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
10.14.9 S ERIES A IDING AND O PPOSING S OURCES Sources of voltage that cause current to flow in the same direction are considered to be series aiding, and their volt-ages are added. Sources of voltage that would tend to force current in opposite directions are said to be series opposing , and the effective source voltage is the difference between the opposing voltages. When two opposing sources are inserted into a circuit, current flow would be in a direction determined by the larger source. Examples of series aiding and opposing sources are shown in Figure 10.39. 10.14.10 K IRCHHOFF ’ S L AW AND M ULTIPLE S OURCE S OLUTIONS Kirchhoff’s law can be used to solve multiple source circuit problems. When applying this method, the exact same pro-cedure is used for multiple-source circuits as was used for single-source circuits. This is demonstrated by the following example. ■ EXAMPLE 10.18 Problem: Find the amount of current in the circuit shown in Figure 10.40. Solution: Start at point A. Basic equation: E a + E b + E c + … + E n = 0 From the circuit: E b 2 + E 1 – E b 1 + E b 3 + E 2 = 0 40 + 40 I – 140 + 20 + 20 I = 0 Combining like terms, we obtain 60 I – 80 = 0 60 I = 80 I = 1.33 amps 10.15 GROUND The term ground is used to denote a common electrical point of zero potential. The reference point of a circuit is always considered to be at zero potential. The earth (ground) is said to be at zero potential. In Figure 10.41, point A is the zero reference or ground and is symbolized as such. Point C is 60 volts positive and point B is 20 volts positive with respect to ground. The common ground for much electrical/electronics equipment is the metal chassis. The value of ground is noted R 1 R 2 Series aiding E 1 E 2 + + – – R 1 R 2 Series opposing E 2 + + – – FIGURE 10.39 Aiding and opposing sources. I E b 1 140 V E b 2 140 v E b 3 20 V R 2 20 ohms + + + – + – + A – – – R 1 40 ohms FIGURE 10.40 Solving for circuit current in a multiple source circuit.
- Frank R. Spellman, Nancy E. Whiting(Authors)
- 2013(Publication Date)
- CRC Press(Publisher)
Using the same idea as above, a problem can be solved in which the current is the unknown quantity. 11.7.6.8 Series Aiding and Opposing Sources Sources of voltage that cause current to flow in the same direction are considered to be series aiding, and their voltages add. Sources of voltage that would tend to force current in opposite directions are said to be series opposing , and the effective source voltage is the difference between the opposing voltages. When two opposing sources are inserted into a circuit, current flow would be in a direc-tion determined by the larger source. Examples of series aiding and opposing sources are shown in Figure 11.36. 11.7.6.9 Kirchhoff’s Law and Multiple Source Solutions Kirchhoff’s law can be used to solve multiple source circuit problems. When applying this method, the exact same procedure is used for multiple source circuits as was used for single source circuits. This is demonstrated by the following example. ■ EXAMPLE 11.32 Problem: Find the amount of current in the circuit shown in Figure 11.37. E 2 20 volts E 2 10 volt s E A 60 volts + – – + + – – + A I E ? FIGURE 11.35 Determining unknown voltage in a series circuit. 274 Handbook of Mathematics and Statistics for the Environment Solution: Start at point A. Basic equation: E a + E b + E c + … + E n = 0 From the circuit: E b 2 + E 1 – E b 1 + E b 3 + E 2 = 0 40 + 40 I – 140 + 20 + 20 I = 0 Combining like terms, we obtain 60 I – 80 = 0 60 I = 80 I = 1.33 amps 11.7.7 P ARALLEL DC C IRCUITS The principles we applied to solving simple series circuit calculations for determining the reactions of such quantities as voltage, current, and resistance can be used in parallel and series–parallel circuits. E 2 + – E 2 + + – – E 1 + – R 1 R 1 R 2 Series Aiding R 2 Series Opposing FIGURE 11.36 Series aiding and opposing sources. R 1 40 ohms E b2 40 v A E b1 140 v + + – – R 2 20 ohms + + – + – – I E b3 20 v FIGURE 11.37 Solving for circuit current in a multiple-source circuit.
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