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CHAPTER 2 Electric Current. Ohm s Law
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Lower wattage resistors are most usually of the carbon type, in which the resistance is formed from a compressed mixture of carbon with a suitable binder, and then encapsulated in a plastic case. In order to better visualize their construction and appearance, several resistors are sketched below in approximately their actual physical size.
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Above is an example of appearance of a 50-ohm, 100-watt, wire-wound resistor, where the symbol  is the capital omega and is read ohms. In the above type, the resistance wire is wound on the ceramic tube, after which the unit is enameled and baked. Problem 11 If a 25-ohm resistor is carrying a current of 1.86 amperes, how many calories of heat must it be able to dissipate every second Problem 12 Noting that 8C 5=9 8F 32 , calculate the resistance of 450 feet of round aluminum wire of 1/2 inch diameter at 868F. (Answer: 0.03188 ohms) Problem 13 A certain length of copper wire is found to have 2.625 ohms of resistance at 308C. What will be its resistance at 408C (Answer: 2.721 ohms) Problem 14 The heating element of a heater is to be made to have 35 ohms of resistance at an operating temperature of 5658C. If Constantan resistance wire of diameter 1 millimeter (one-thousandth of a meter) is available, how many feet should be cut from a spool of wire at 208C Assume L and A are independent of temperature. (Answer: 183.056 feet)
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The Series Circuit
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A SERIES CIRCUIT or series-connected circuit is a circuit having JUST ONE CURRENT PATH. Thus, Fig. 23 is an example of a series circuit in which a battery of constant potential di erence V volts, and three resistances, are all connected in series.
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CHAPTER 2 Electric Current. Ohm s Law
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Fig. 23
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Since a series circuit has just one current path, it follows that all the components in a series circuit CARRY THE SAME CURRENT I, a fact evident from inspection of Fig. 23. As explained in section 2.1, the current I is assumed to be a ow of positive charge, and thus ows out of the positive terminal of the battery and around through the external circuit, reentering the battery at the negative terminal. This is indicated by the arrows in Fig. 23. In a series circuit, the TOTAL resistance, RT , that the battery sees is equal to the SUM of the individual resistances. Thus, in the particular case of Fig. 23 the battery sees a total resistance, RT R1 R2 R3 , while in the general case of n resistances connected in series the battery sees a total resistance of RT R1 R2 R3 Rn By Ohm s law, eq. (11), it follows that the current I in a series circuit is equal to I V V RT R1 R2 Rn 21 20
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In the above, we re assuming the resistances of the copper connecting wires to be negligibly small in comparison with RT , and this will be normally true in practical circuit work. (If such is not the case, then, in Fig. 23 for example, a fourth resistance would be added in series in the diagram, equal to the resistance of the connecting wires; but this will seldom be necessary.) We have seen that a battery is a device capable of moving electric charge against the internal electric eld that exists between its positive and negative terminals. As explained in section 2.2, a battery can do this because it is able to convert chemical energy into electrical energy. A battery is thus referred to as a generator, and is classi ed as an ACTIVE device, because it is a source of electrical energy. Resistance, on the other hand, consumes electrical energy, removing it from the circuit in the form of heat. Since resistance does not produce or generate electrical energy, it is a non-active or PASSIVE type of circuit element. A resistor, being a passive device, has no internal electric eld until it is connected to a battery. When this is done, an internal electric eld appears between the terminals of the resistor, a potential di erence exists between the terminals, and current begins to ow. The potential di erence between the terminals of a resistor is called the VOLTAGE DROP across the resistor, and, by eq. (13), is equal to the current I times the resistance R; that is, the voltage drop across a resistance of R ohms carrying a current of I amperes is
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