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When an ac voltage is placed across an inductor and starts to increase (either positively or negatively) from zero, it takes a fraction of a cycle for the current to follow. Once the voltage starts decreasing from its maximum peak (either positive or negative) in the cycle, it again takes a fraction of a cycle for the current to follow. The instantaneous current can t quite keep up with the instantaneous voltage, as it does in a pure resistance. Thus, in a circuit containing inductive reactance, the current is said to lag the voltage in phase.

Suppose a coil has an inductance of 0. 50 H, and the frequency of the ac passing through it is 60 Hz. What is the inductive reactance Using the above formula, XL 6.28 60 0. 50 188.4 ohms. You should round this off to two significant digits, or 190 ohms, because the inductance and frequency are both expressed to only two significant digits.

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Pure Inductance Suppose that you place an ac voltage across a coil, with a frequency high enough so that the inductive reactance, XL, is much larger than the resistance, R. In this situation, the current is 1 4 of a cycle behind the voltage. That is, the current lags the voltage by 90 , as shown in Fig. 13-8. At very low frequencies, large inductances are normally needed in order for the current lag to be

Problem 13-2

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a full 90 . This is because any coil has some resistance; no wire is a perfect conductor. If some wire were found that had a mathematically zero resistance, and if a coil of any size were wound from this wire, then the current would lag the voltage by 90 in this inductor, no matter what the ac frequency. When the value of XL is very large compared with the value of R in a circuit that is, when there is an essentially pure inductive reactance the vector in the RL plane points straight up along the XL axis. Its angle is 90 from the R axis, which is considered the zero line in the RL plane.

What will be the inductive reactance of the above coil if the supply is a battery that supplies pure dc Because dc has a frequency of zero, XL 6.28 0 0. 50 0. That is, there will be no inductive reactance. Inductance doesn t generally have any practical effect with pure dc.

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Inductance with Resistance When the resistance in a resistance-inductance (RL) circuit is significant compared with the inductive reactance, the current lags the voltage by something less than 90 (Fig. 13-9). If R is small compared with XL, the current lag is almost 90 , but as R gets larger relative to XL, the lag decreases. The value of R in an RL circuit can increase relative to XL because resistance is deliberately placed in series with the inductance. It can also happen because the ac frequency gets so low that XL

Problem 13-3

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