Voltage Dividers and Current Dividers

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Presentation transcript:

Voltage Dividers and Current Dividers Chapter 7 Voltage Dividers and Current Dividers Topics Covered in Chapter 7 7-1: Series Voltage Dividers 7-2: Current Dividers with Two Parallel Resistances 7-3: Current Division by Parallel Conductances 7-4: Series Voltage Divider with Parallel Load Current 7-5: Design of a Loaded Voltage Divider

7-1: Series Voltage Dividers VT is divided into IR voltage drops that are proportional to the series resistance values. Each resistance provides an IR voltage drop equal to its proportional part of the applied voltage: VR = (R/RT) × VT This formula can be used for any number of series resistances because of the direct proportion between each voltage drop V and its resistance R. The largest series R has the largest IR voltage drop. McGraw-Hill © 2007 The McGraw-Hill Companies, Inc. All rights reserved.

7-1: Series Voltage Dividers The Largest Series R Has the Most V. VR1 = R1 RT × VT = 1 kW 1000 kW × 1000 V = 1 V VR2 = R2 RT × VT 999 kW 1000 kW = × 1000 V = 999 V Fig. 7-2a: Example of a very small R1 in series with a large R2; VR2 is almost equal to the whole VT. KVL check: 1 V + 999 V = 1000 V Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

7-1: Series Voltage Dividers Voltage Taps in a Series Voltage Divider Different voltages are available at voltage taps A, B, and C. The voltage at each tap point is measured with respect to ground. Ground is the reference point. Fig. 7-2b: Series voltage divider with voltage taps. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

7-1: Series Voltage Dividers Voltage Taps in a Series Voltage Divider Note: VAG is the sum of the voltage across R2, R3, and R4. VAG is one-half of the applied voltage VT, because R2+R3+ R4 = 50% of RT VBG = 2.5 kW 20 kW × 24 V = 3 V VAG = 12 V VCG = 1 kW 20 kW × 24 V = 1.2 V Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

7-1: Series Voltage Dividers

7-2: Current Dividers with Two Parallel Resistances IT is divided into individual branch currents. Each branch current is inversely proportional to the branch resistance value. For two resistors, R1 and R2, in parallel: Note that this formula can only be used for two branch resistances. The largest current flows in the branch that has the smallest R.

7-2: Current Dividers with Two Parallel Resistances I1 = 4 Ω/(2 Ω + 4 Ω) × 30A = 20A I2= 2 Ω /(2 Ω + 4 Ω) × 30A = 10A Fig. 7-3: Current divider with two branch resistances. Each branch I is inversely proportional to its R. The smaller R has more I. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.