Chapter 20 Inductive Reactance Topics Covered in Chapter

Chapter 20 Inductive Reactance Topics Covered in Chapter 20 20 -1: How XL Reduces the Amount of I 20 -2: XL = 2πf. L 20 -3: Series or Parallel Inductive Reactances 20 -4: Ohm's Law Applied to XL 20 -5: Applications of XL for Different Frequencies 20 -6: Waveshape of v. L Induced by Sine-Wave Current Mc. Graw-Hill © 2015 The Mc. Graw-Hill Companies, Inc. All rights reserved.

20 -1: HOW XL REDUCES THE AMOUNT OF I An inductance can have appreciable XL in ac circuits to reduce the amount of current. The higher the frequency of ac, and the greater the L, the higher the XL. There is no XL for steady direct current. In this case, the coil is a resistance equal to the resistance of the wire.

20 -1: HOW XL REDUCES THE AMOUNT OF I § In Fig. 20 -1 (a), there is no inductance, and the ac voltage source causes the bulb to light with full brilliance. § In Fig. 20 -1 (b), a coil is connected in series with the bulb. § The coil has a negligible dc resistance of 1 Ω, but a reactance of 1000 Ω. § Now, I is 120 V / 1000 Ω, approximately 0. 12 A. This is not enough to light the bulb. § In Fig. 20 -1 (c), the coil is also in series with the bulb, but the battery voltage produces a steady dc. § Without any current variations, there is no XLand the bulb lights with full brilliance. Fig. 20 -1: Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

20 -2: XL = 2ΠFL The formula XL = 2πf. L includes the effects of frequency and inductance for calculating the inductive reactance. The frequency is in hertz, and L is in henrys for an XL in ohms. The constant factor 2π is always 2 x 3. 14 = 6. 28. The frequency f is a time element. The inductance L indicates the physical factors of the coil. Inductive reactance XL is in ohms, corresponding to a VL/IL ratio for sine-wave ac circuits.

20 -3: SERIES OR PARALLEL INDUCTIVE REACTANCES § Since reactance is an opposition in ohms, the values XL in series or in parallel are combined the same way as ohms of resistance. § With series reactances, the total is the sum of the individual values as shown in Fig. 20 -5 (a). § The combined reactance of parallel reactances is calculated by the reciprocal formula. Fig. 20 -5

20 -4: OHM'S LAW APPLIED TO XL The amount of current in an ac circuit with only inductive reactance is equal to the applied voltage divided by XL. I = V/XL = 1 A I = V/XLT = 0. 5 A Fig. 20 -6: I 1 = V/XL 1 = 1 A I 2 = V/XL 2 = 1 A IT = I 1 + I 2 = 2 A Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

20 -5: APPLICATIONS OF XL FOR DIFFERENT FREQUENCIES The general use of inductance is to provide minimum reactance for relatively low frequencies but more for higher frequencies. If 1000 Ω is taken as a suitable value of XL for many applications, typical inductances can be calculated for different frequencies. Some are as follows: 2. 65 H 160 m. H frequency 16 m. H 60 Hz 10, 000 Hz Power-line frequency Medium audio 10, 000 Hz High audio frequency

20 -6: WAVESHAPE OF VL INDUCED BY SINE-WAVE CURRENT Induced voltage depends on rate of change of current rather than on the absolute value of i. A v. L curve that is 90° out of phase is a cosine wave of voltage for the sine wave of current i. L. The frequency of VL is 1/T. The ratio of v. L/i. L specifies the inductive reactance in ohms.

20 -6: WAVESHAPE OF VL INDUCED BY SINE-WAVE CURRENT di/dt for Sinusoidal Current is a Cosine Wave di/dt Current v. L = L di dt 0 Sinusoidal Current Iinst. = Imax × cos Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

20 -6: WAVESHAPE OF VL INDUCED BY SINE-WAVE CURRENT Amplitude Inductor Voltage and Current 0 Time Θ = -90 V I Copyright © The Mc. Graw-Hill Companies, Inc. Permission required for reproduction or display.

20 -6: WAVESHAPE OF VL INDUCED BY SINE-WAVE CURRENT Application of the 90° phase angle in a circuit The phase angle of 90° between VL and I will always apply for any L with sine wave current. The specific comparison is only between the induced voltage across any one coil and the current flowing in its turns.

20 -6: WAVESHAPE OF VL INDUCED BY SINE-WAVE CURRENT § Current I 1 lags VL 1 by 90°. § Current I 2 lags VL 2 by 90°. § Current I 3 lags VL 3 by 90°. NOTE: I 3 is also IT for the seriesparallel circuit. Fig. 20 -8