2Summary Summary Combination circuits Most practical circuits have combinations of series and parallel components. You can frequently simplify analysis by combining series and parallel components.An important analysis method is to form an equivalent circuit. An equivalent circuit is one that hascharacteristics that are electrically the same as another circuit but is generally simpler.
3Summary Summary Combination circuits For example: is equivalent to There are no electrical measurements that can distinguish the boxes.
4Summary Summary Combination circuits Another example: is equivalent to There are no electrical measurements that can distinguish the boxes.
5Summary Summary is equivalent to is equivalent to There are no electrical measurements that can distinguish between the three boxes.
6Summary Summary Combination circuits Kirchhoff’s voltage law and Kirchhoff’s current law can be applied to any circuit, including combination circuits.So will this path!For example, applying KVL, the path shown will have a sum of 0 V.
7SummarySummaryKirchoff’s current law can also be applied to the same circuit. What are the readings for node A?
8Summary Summary Combination circuit Tabulating current, resistance, voltage and power is a useful way to summarize parameters. Solve for the unknown quantities in the circuit shown.I1= R1= 270 W V1= P1=21.6 mA5.82 V126 mWI2= R2= 330 W V2= P2=12.7 mA4.18 V53.1 mWI3= R3= 470 W V3= P3=8.9 mA4.18 V37.2 mWIT= RT= VS= 10 V PT=21.6 mA464 W216 mW
9SummarySummaryKirchhoff’s laws can be applied as a check on the answer.equal to the sum of the branch currents in R2 and R3.Notice that the current in R1 isThe sum of the voltages around the outside loop is zero.I1= R1= 270 W V1= P1=21.6 mA5.82 V126 mWI2= R2= 330 W V2= P2=12.7 mA4.18 V53.1 mWI3= R3= 470 W V3= P3=8.9 mA4.18 V37.2 mWIT= RT= VS= 10 V PT=21.6 mA464 W216 mW
10Summary Summary 4.04 V 10 V Loading effect of a voltmeter 4.04 V Assume VS = 10 V, but the meter reads only 4.04 V when it is across either R1 or R2.Can you explain what is happening?All measurements affect the quantity being measured. A voltmeter has internal resistance, which can change the resistance of the circuit under test. In this case, a 1 MW internal resistance of the meter accounts for the readings.
11Summary Summary Wheatstone bridge The Wheatstone bridge consists of four resistive arms forming two voltage dividers and a dc voltage source. The output is taken between the dividers. Frequently, one of the bridge resistors is adjustable.When the bridge is balanced, the output voltage iszero,and the products of resistances in the opposite diagonal arms areequal.
12Summary Summary Summary Wheatstone bridge Example: What is the value of R2 if the bridge is balanced?330 W470 W12 V384 W270 W
13Key Terms Balanced bridge Bleeder currentLoadA bridge circuit that is in the balanced state is indicated by 0 V across the output.The current left after the load current is subtracted from the total current into the circuit.An element (resistor or other component) connected across the output terminals of a circuit that draws current from the circuit.
14Key Terms Unbalanced bridge Wheatstone bridgeA bridge circuit that is in the unbalanced state is indicated by a voltage across the output that is proportional to the amount of deviation from the balanced state.A 4-legged type of bridge circuit with which an unknown resistance can be accurately measured using the balanced state. Deviations in resistance can be measured using the unbalanced state.
15Quiz 1. Two circuits that are equivalent have the same a. number of componentsb. response to an electrical stimulusc. internal power dissipationd. all of the above
16Quiz2. If a series equivalent circuit is drawn for a complex circuit, the equivalent circuit can be analyzed witha. the voltage divider theoremb. Kirchhoff’s voltage lawc. both of the aboved. none of the above
17Quiz 3. For the circuit shown, a. R1 is in series with R2 b. R1 is in parallel with R2c. R2 is in series with R3d. R2 is in parallel with R3
18Quiz 4. For the circuit shown, a. R1 is in series with R2 b. R4 is in parallel with R1c. R2 is in parallel with R3d. none of the above
19Quiz 5. The total resistance, RT, of the group of resistors is a. 1.0 kWb. 2.0 kWc. 3.0 kWd. 4.0 kW
20Quiz 6. For the circuit shown, Kirchhoff's voltage law a. applies only to the outside loopb. applies only to the A junction.c. can be applied to any closed path.d. does not apply.
21Quiz7. The effect of changing a measured quantity due to connecting an instrument to a circuit is calleda. loadingb. clippingc. distortiond. loss of precision
22Quiz8. An unbalanced Wheatstone bridge has the voltages shown. The voltage across R4 isa. 4.0 Vb. 5.0 Vc. 6.0 Vd. 7.0 V
23Quiz9. Assume R2 is adjusted until the Wheatstone bridge is balanced. At this point, the voltage across R4 is measured and found to be 5.0 V. The voltage across R1 will bea. 4.0 Vb. 5.0 Vc. 6.0 Vd. 7.0 V
24Quiz10. For the circuit shown, if R3 opens, the voltage at point A willa. decreaseb. stay the same.c. increase.