Introduction to Series-Parallel DC Circuits. Online Resource for ETCH 213 Faculty: B. Allen

Transcription

1 Introduction to Series-Parallel DC Circuits

2 Series-parallel circuit A network or circuit that contains components that are connected in both series and parallel.

3 Series-parallel resistive circuits

4 Tracking current through a series-parallel circuit

5 Total resistance in a seriesparallel circuit Step 1: Determine the equivalent resistance of all branch series-connected resistors. Step 2: Determine the equivalent resistance of all parallel-connected combinations. Step 3: Determine the equivalent resistance of the remaining series-connected resistors.

6 Calculating total resistance Find the equivalent resistance for R 5 and R 6.

7 Find the equivalent resistance for R 4 and R 5-6.

8 Find the equivalent resistance for R 2, R 3, and R

9 Find R T.

10 Voltage division in a seriesparallel circuit Find: V1 V2 V3 V4 V5 V6 V7

11 Find R 3-4 and R R 3-4 = R 3 + R 4 = 2kohm R = 1kohm/3 = 333 ohm

12 Find R R = R 2 R 3-4 /(R 2 + R 3-4 ) = 1k 2k/(1k + 2k) = 667ohm

13 Find R T, V 1, V 2-3-4, V R T = 1k +667ohm +333ohm = 2kohm V 1 = R 1 /R T V T = 1k/2k 12V = 6V V = R /R T 12V = 667/2k 12V = 4V V = R /R T 12V = 333/2k 12V = 2V

14 Voltage division in a seriesparallel circuit. Summary Find: V1 = 6V V2 = 4V V3 = 2V V4 = 2V V5 = 2V V6 = 2V V7 = 2V

15 Branch current in a seriesparallel circuit Find: I1 I2 I3 I4 I5 I6 I7

16 Find total current Since R T = 2kohm, I T = V T /R T = 12V/2kohm = 6mA. I 1 = 6mA.

17 Find I 2, I 3, I 4 I 2 = R /R 2 I T = 667ohm/1k 6mA = 4 ma I 3 = I 4 = R /R 3-4 I T = 667ohm/2kohm 6mA = 2mA

18 Find I 5, I 6, I 7 I 5 = R /R 5 I T = 330ohm/1kohm 6mA = 2mA I 6 = R /R 6 I T = 330ohm/1kohm 6mA = 2mA I 7 = R /R 7 I T = 330ohm/1kohm 6mA = 2mA

19 Branch current in a seriesparallel circuit: Summary Find: I1 = 6mA I2 = 4mA I3 = 2mA I4 = 2mA I5 = 2mA I6 = 2mA I7 = 2mA

20 Power in a series-parallel P T = P 1 + P 2 + P 3 + circuit

21 Five-step procedure for seriesparallel circuit analysis Step 1: Determine the total resistance. Step 2: Determine the total current. Step 3: Determine the voltage across each series resistor and each parallel combination of resistors. Step 4: Determine the value of current through each parallel resistor in every parallel combination. Step 5: Determine the total and individual power dissipated by the circuit.

22 Loading of voltage-divider circuits Loading The adding of a load to a source

23 The Wheatstone bridge

24 Balanced Wheatstone bridge

25 Unbalanced Wheatstone bridge When the voltmeter in a bridge circuit does not read zero, the bridge is unbalanced.

26 Determining an unknown resistor using a bridge circuit Using a bridge circuit with a variable resistor, force the voltmeter to read zero. This will balance the bridge and the value of the variable resistor will equal the value of the unknown resistor.

27 R-2R ladder circuits R-2R A network or circuit composed of a sequence of L networks connected in tandem. This R-2R circuit is used in digital-to-analog converters.

28 Simplification of R 2R ladder circuit

29 Troubleshooting series-parallel circuits An open in a series component No current flow An open in a parallel component Current A short in a series component Current A short in a parallel component Current

30 Theorems for DC circuits Superposition Theorem Thevenin s Theorem Norton s Theorem

31 Voltage and current sources Voltage Source The circuit or device that supplies voltage to a load circuit. Current Source The circuit or device that supplies current to a load circuit.

32 Superposition Theorem In a network or circuit containing two or more voltage sources, the current at any point is equal to the algebraic sum of the individual source currents produced by each source acting separately.

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34 Thevenin s Theorem Any network of voltage sources and resistors can be replaced by a single equivalent voltage source (V TH ) in series with a single equivalent resistance (R TH ).

35 To Thevenize a circuit Identify the circuit to be Thevenized. Measure the voltage at the output. This is the V TH. Remove the sources and replace them with a short; measure the resistance at the output. This is the R TH.

36 Find the Thevenin equivalent circuit for:

37 Thevenin equivalent circuit

38 Find V TH. V TH = 1.33V

39 Find R TH. R TH = 2kohm

40 Norton s Theorem Any network of voltage sources and resistors can be replaced by a single equivalent current source, I N, in parallel with a single equivalent resistance, R N.

41 To find the equivalent Norton circuit Identify the circuit for a Norton equivalent circuit. Measure the the short circuit amperes. This is I N. Replace the sources with shorts and measure the resistance at the output. This is R N.

42 Find the Norton equivalent circuit for:

43 Norton equivalent circuit

44 Find I N. I N = mA

45 Find R N. R N = 2.0kohm

46 End of Introduction to Series-Parallel DC Circuits