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It is impractical to make wire loops 1 million miles in circumference. But lengths of wire can be coiled up. When this is done, the magnetic flux is increased for a given length of wire compared with the flux produced by a single-turn loop. The magnetic flux density inside a coil is multiplied when a ferromagnetic core is placed within it. The increase in flux density has the effect of increasing the inductance, too, so L is many times greater with a ferromagnetic core than with an air core or a nonmagnetic core such as plastic or wood. The current that an inductor can handle depends on the diameter (gauge) of the wire. But the value of L is a function of the number of turns in the coil, the diameter of the coil itself, and the overall shape of the coil. In general, the inductance of a coil is directly proportional to the number of turns of wire. Inductance is directly proportional to the diameter of the coil. The length of a coil, given a certain number of turns and a certain diameter, has an effect as well. If a coil having a certain number of turns and a certain diameter is stretched out, its inductance decreases. Conversely, if it is squashed up, its inductance increases.
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When a battery is first connected across an inductor, the current builds up at a rate that depends on the inductance. The greater the inductance, the slower the rate of current buildup for a given battery voltage. The unit of inductance is an expression of the ratio between the rate of current buildup and the voltage across an inductor. An inductance of 1 henry (1 H) represents a potential difference of 1 volt (1 V) across an inductor within which the current is changing at the rate of 1 ampere per second (1 A/s). The henry is a huge unit of inductance. You won t often see an inductor this large, although some power-supply filter chokes have inductances up to several henrys. Usually, inductances are expressed in millihenrys (mH), microhenrys ( H), or nanohenrys (nH). You should know your prefix multipliers by now, but in case you ve forgotten: 1 mH = 0.001 H = 10 3 H 1 H = 0.001 mH = 10 6 H 1 nH = 0.001 H = 10 9 H Small coils with few turns of wire produce small inductances, in which the current changes quickly and the induced voltages are small. Large coils with ferromagnetic cores, and having many turns of wire, have high inductances in which the current changes slowly and the induced voltages are large. The current from a battery, building up or dying down through a high-L coil, can give rise to a deadly potential difference between the end terminals of the coil many times the voltage of the battery itself. This is how spark coils work in internal combustion engines. Be careful around them!
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When the magnetic fields around inductors do not interact, inductances in series add like resistances in series. The total value is the sum of the individual values. It s important to be sure that you are using the same size units for all the inductors when you add their values. After that, you can convert the result to any inductance unit you want.
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Problem 10-1 Suppose three 40.0- H inductors are connected in series, and there is no interaction, or mutual inductance, among them (Fig. 10-3). What is the total inductance
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simply add up, as long as the inductors do not interact.
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Inductors in Parallel 163
Add up the values. Call the inductances of the individual components L1, L2, and L3, and the total inductance L. Then L = L1 + L2 + L3 = 40.0 + 40.0 + 40.0 = 120 H.
Problem 10-2 Imagine three inductors, with no mutual inductance, with values of 20.0 mH, 55.0 H, and 400 nH. What is the total inductance, in millihenrys, of these components if they are connected in series as shown in Fig. 10-3 First, convert all the inductances to the same units. Microhenrys are a good choice because that unit makes the calculation process the least messy. Call L1 = 20.0 mH = 20,000 H, L2 = 55.0 H, and L3 = 400 nH = 0.400 H. The total inductance is therefore L = 20,000 + 55.0 + 0.400 = 20,055.4 H. This is 20.1 mH after converting and rounding off.
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