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barcode printing using vb.net Vectors in the RL Plane in Software
Vectors in the RL Plane Recognize QR Code 2d Barcode In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Print Quick Response Code In None Using Barcode maker for Software Control to generate, create Denso QR Bar Code image in Software applications. Engineers sometimes like to represent points in the RL plane (and in other types of coordinate planes, too) as vectors. This gives each point a definite magnitude and a precise direction. Decoding QR Code 2d Barcode In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. QR Code ISO/IEC18004 Drawer In Visual C# Using Barcode encoder for .NET framework Control to generate, create QR Code image in VS .NET applications. 236 Inductive reactance
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Denso QR Bar Code Encoder In VB.NET Using Barcode maker for .NET framework Control to generate, create Denso QR Bar Code image in Visual Studio .NET applications. Data Matrix Encoder In None Using Barcode maker for Software Control to generate, create DataMatrix image in Software applications. In Fig. 136, there are four different points shown. Each one is represented by a certain distance to the right of the origin (0,0), and a specific distance upwards from the origin. The first of these is the resistance, R, and the second is the inductive reactance, XL. Thus, the RL combination is a twodimensional quantity. There is no way to uniquely define RL combinations as single numbers, or scalars, because there are two different quantities that can vary independently. Another way to think of these points is to draw lines from the origin out to them. Then you can think of the points as rays, each having a certain length, or magnitude, and a definite direction, or angle counterclockwise from the resistance axis. These rays, going out to the points, are vectors (Fig. 137). You ve already been introduced to these things. Vectors seem to engender apprehension in some people, as if they were invented by scientists for the perverse pleasure of befuddling ordinary folks. What are you taking this semester asks Jane. Vector analysis! Joe shudders (if he s one of the timid types), or beams (if he wants to impress Jane). This attitude is completely groundless. Just think of vectors as arrows that have a certain length, and that point in some direction. In Fig. 137, the points of Fig. 136 are shown as vectors. The only difference is that there is some more ink on the paper. Creating UPCA In None Using Barcode generator for Software Control to generate, create UCC  12 image in Software applications. Create GS1  13 In None Using Barcode printer for Software Control to generate, create EAN13 Supplement 5 image in Software applications. Current lags voltage 237
Encoding EAN 128 In None Using Barcode creation for Software Control to generate, create EAN128 image in Software applications. Making Bar Code In None Using Barcode encoder for Software Control to generate, create barcode image in Software applications. 137 Four vectors in the RL impedance plane.
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DataMatrix Creation In C#.NET Using Barcode drawer for .NET Control to generate, create DataMatrix image in Visual Studio .NET applications. Generate Bar Code In Java Using Barcode creator for Eclipse BIRT Control to generate, create barcode image in Eclipse BIRT applications. Inductance, as you recall, stores electrical energy as a magnetic field. When a voltage is placed across a coil, it takes awhile for the current to build up to full value. When ac is placed across a coil, the current lags the voltage in phase. Scan Bar Code In Visual Basic .NET Using Barcode reader for VS .NET Control to read, scan read, scan image in .NET framework applications. Painting Barcode In Java Using Barcode generation for Java Control to generate, create barcode image in Java applications. Pure inductance
Make Code 128A In ObjectiveC Using Barcode generator for iPad Control to generate, create Code 128 Code Set B image in iPad applications. Make EAN / UCC  13 In Visual Studio .NET Using Barcode generator for Reporting Service Control to generate, create UCC  12 image in Reporting Service applications. Suppose that you place an ac voltage across a lowloss 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 onequarter of a cycle behind the voltage. That is, the current lags the voltage by 90 degrees (Fig. 138). At very low frequencies, large inductances are normally needed in order for this current lag to be a full 1 4 cycle. 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 degrees 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 inductance the vector in the RL plane points straight up along the XL axis. Its angle is 90 degrees from the R axis, which is considered the zero line in the RL plane. 238 Inductive reactance
138 In a pure inductance, the current lags the voltage by 90 degrees.
Inductance and resistance
When the resistance in a resistanceinductance circuit is significant compared with the inductive reactance, the current lags the voltage by something less than 90 degrees (Fig. 139). If R is small compared with XL, the current lag is almost 90 degrees; as R gets larger, the lag decreases. A circuit with resistance and inductance is called an RL circuit. The value of R in an RL circuit might increase relative to XL because resistance is deliberately placed in series with the inductance. Or, it might happen because the ac frequency gets so low that XL decreases until it is in the same ball park with the loss resistance R in the coil winding. In either case, the situation can be schematically represented by a coil in series with a resistor (Fig. 1310). If you know the values of XL and R, you can find the angle of lag, also called the RL phase angle, by plotting the point R jXL on the RL plane, drawing the vector from the origin 0 j0 out to that point, and then measuring the angle of the vector, counterclockwise from the resistance axis. You can use a protractor to measure this angle, or you can compute its value using trigonometry. In fact, you don t need to know the actual values of XL and R in order to find the angle of lag. All you need to know is their ratio. For example, if L 5 and R 3 , you will get the same angle as you would get if XL 50 and R 30 , or if XL 20 and R 12 . The angle of lag will be the same for any values of XL and R in the ratio of 5:3. It s easy to find the angle of lag whenever you know the ratio of R to XL. You ll see some examples shortly.

