Series-Parallel Circuits. Objectives

Transcription

1 Series-Parallel Circuits Objectives Identify series-parallel configuration Analyze series-parallel circuits Apply KVL and KCL to the series-parallel circuits Analyze loaded voltage dividers Determine the loading effect of a voltmeter on a circuit Analyze a Wheatstone bridge circuit 5 February 2004 Series-Parallel Circuits 2 Professor Andrew H. Andersen 1

2 Analysis of Series-Parallel Circuits Determine total resistance seen by the source Determine all branch currents and the source current Determine all voltage drops 5 February 2004 Series-Parallel Circuits 3 Total Resistance Identify the parallel resistances, and calculate the equivalent resistance(s) Identify the series resistance, and calculate the total resistance for the circuit 5 February 2004 Series-Parallel Circuits 4 Professor Andrew H. Andersen 2

3 Find RT R = R + R AB 1 4 R 2R 3 R 2+ R 3 R = R = R + R R BC = T AC AB BC 5 February 2004 Series-Parallel Circuits 5 Resistance in the Series-Parallel Circuit 5 February 2004 Series-Parallel Circuits 6 Professor Andrew H. Andersen 3

4 Resistance in the Series-Parallel Circuit 5 February 2004 Series-Parallel Circuits 7 Identify the Nodes and Redraw Circuit 5 February 2004 Series-Parallel Circuits 8 Professor Andrew H. Andersen 4

5 Redrawn Circuit from Slide 8 5 February 2004 Series-Parallel Circuits 9 Current in the Series-Parallel Circuit Using the total resistance and the source voltage, find the total current by applying Ohm s law I T = V R S T Using the current-divider formula, Kirchhoff s current law (KCL), Ohm s law, or combinations of these, you can find the current in any branch of a series-parallel circuit 5 February 2004 Series-Parallel Circuits 10 Professor Andrew H. Andersen 5

6 Write the KCL Equation for Node A 5 February 2004 Series-Parallel Circuits 11 Apply KCL to Each Node At Node B I2 = I3 + I4 At Node A IT = I1 + I2 At Node C IT = I1 + I3 + I4 5 February 2004 Series-Parallel Circuits 12 Professor Andrew H. Andersen 6

7 Apply KVL to the Series-Parallel Circuit 5 February 2004 Series-Parallel Circuits 13 KVL in the Series-Parallel Circuit VS = VAB + VBC VBC = VR4 + VR5 = VR3 5 February 2004 Series-Parallel Circuits 14 Professor Andrew H. Andersen 7

8 Unloaded Voltage Dividers A voltage divider produces an output which depends upon the values of the dividing resistors All resistors in an unloaded voltage divider are connected in series This voltage is the unloaded output voltage 5 February 2004 Series-Parallel Circuits 15 Loaded Voltage Dividers When a load resistor RL is connected between the output terminal and ground, the output voltage is reduced by an amount that depends on the value of RL Solve the circuit for RT between node A and ground. Then solve for the desired voltages or currents 5 February 2004 Series-Parallel Circuits 16 Professor Andrew H. Andersen 8

9 Load Current and Bleeder Current Bleeder current is the current left (I3) after the total load current is subtracted from the total current into the circuit In Power Supply circuits, R3 is used to discharge the filter capacitor when power is removed. 5 February 2004 Series-Parallel Circuits 17 Loading Effect of a Voltmeter When measuring across a resistor, a voltmeter is connected in parallel with the resistor Being in parallel, the internal resistance of the voltmeter will have a loading effect on the circuit that is being measured Modern digital voltmeters (DMM) have an internal resistance of 10MΩ 5 February 2004 Series-Parallel Circuits 18 Professor Andrew H. Andersen 9

10 Loading Effect of a Voltmeter If the meter resistance is at least one hundred times greater than the resistance across which it is connected, the loading effect can be neglected the measurement error is less than 1% 5 February 2004 Series-Parallel Circuits 19 Analog Voltmeter Loading In the circuits above, R2 in circuit C is most affected by the Voltmeter Loading, and least affected by circuit A 5 February 2004 Series-Parallel Circuits 20 Professor Andrew H. Andersen 10

11 Wheatstone Bridge A Wheatstone bridge is used to precisely measure resistance A Wheatstone bridge is also applied with transducer measurements, to measure physical quantities such as temperature, strain, and pressure, where small transducer resistance changes may need to be precisely measured Tiny changes in transducer resistance will unbalance the bridge, thereby providing a measurement reading 5 February 2004 Series-Parallel Circuits 21 Wheatstone Bridge with Transducer Input 5 February 2004 Series-Parallel Circuits 22 Professor Andrew H. Andersen 11

12 Temperature Transducer 5 February 2004 Series-Parallel Circuits 23 Balancing the Bridge for 0V Output 5 February 2004 Series-Parallel Circuits 24 Professor Andrew H. Andersen 12

13 Find All Currents and Voltages 5 February 2004 Series-Parallel Circuits 25 Find VL for Each Position of the Switch 5 February 2004 Series-Parallel Circuits 26 Professor Andrew H. Andersen 13