To learn to calculate the equivalent resistance of the circuits combining series and parallel resistors. Resistors are o
Posted: Mon Jul 18, 2022 5:56 am
To learn to calculate the equivalent resistance of the circuitscombining series and parallel resistors.
Resistors are often connected to each other in electriccircuits. Finding the equivalent resistance ofcombinations of resistors is a common and important task.Equivalent resistance is defined as the single resistance that canreplace the given combination of resistors in such a manner thatthe currents in the rest of the circuit do not change.Finding the equivalent resistance is relatively straighforward ifthe circuit contains only resistors in series and parallel.An example of resistors connected in seriesis shown in the diagram:
(Figure 1)
For such a connection, the current is the same for allindividual resistors and the total voltage is the sum of thevoltages across the individual resistors.Using Ohm's law (R=VIR=VI ), one canshow that, for resistors in series, the equivalent resistance isthe sum of the individual resistances.Mathematically, these relationships can be written as:
I=I1=I2=I3=...I=I1=I2=I3=...
V=V1+V2+V3+...V=V1+V2+V3+...
Req−series=R1+R2+R3+...Req−series=R1+R2+R3+...
An example of resistors connected in parallelis shown in the diagram.
For resistors connected in parallel the voltageis the same for all individual resistors because they are allconnected to the same two points (A and B on the diagram). Thetotal current is the sum of the currents through the individualresistors. This should makes sense as the total current "splits" atpoints A and B.Using Ohm's law, one can show that, for resistors connected inparallel, the reciprocal of the equivalent resistance is the sum ofthe reciprocals of the individual resistances.Mathematically, these relationships can be written as:
V=V1=V2=V3=...V=V1=V2=V3=...
I=I1+I2+I3+...I=I1+I2+I3+...
1Req−parallel=1R1+1R2+1R3+...1Req−parallel=1R1+1R2+1R3+...
NOTE: If you have already studied capacitors and therules for finding the equivalent capacitance, you should noticethat the rules for the capacitors are similar - but not quite thesame as the ones discussed here.In this problem, you will use the the equivalent resistanceformulas to determine ReqReqR_eq for various combinationsof resistors.
1 of 4The figure represents three resistors, labeled as R 1, R2, and R 3, connected in series from left to right. There is acurrent I flowing from left to right through them.
Part A
Part complete
For the combination of resistors shown, find the equivalentresistance between points A and B.(Figure 3)
Express your answer in Ohms.
--
SubmitPrevious AnswersRequest Answer
Part B
Part complete
For the set-up shown, find the equivalent resistance betweenpoints A and B.(Figure 4)
Express your answer in Ohms.
--
nothing
Resistors are often connected to each other in electriccircuits. Finding the equivalent resistance ofcombinations of resistors is a common and important task.Equivalent resistance is defined as the single resistance that canreplace the given combination of resistors in such a manner thatthe currents in the rest of the circuit do not change.Finding the equivalent resistance is relatively straighforward ifthe circuit contains only resistors in series and parallel.An example of resistors connected in seriesis shown in the diagram:
(Figure 1)
For such a connection, the current is the same for allindividual resistors and the total voltage is the sum of thevoltages across the individual resistors.Using Ohm's law (R=VIR=VI ), one canshow that, for resistors in series, the equivalent resistance isthe sum of the individual resistances.Mathematically, these relationships can be written as:
I=I1=I2=I3=...I=I1=I2=I3=...
V=V1+V2+V3+...V=V1+V2+V3+...
Req−series=R1+R2+R3+...Req−series=R1+R2+R3+...
An example of resistors connected in parallelis shown in the diagram.
For resistors connected in parallel the voltageis the same for all individual resistors because they are allconnected to the same two points (A and B on the diagram). Thetotal current is the sum of the currents through the individualresistors. This should makes sense as the total current "splits" atpoints A and B.Using Ohm's law, one can show that, for resistors connected inparallel, the reciprocal of the equivalent resistance is the sum ofthe reciprocals of the individual resistances.Mathematically, these relationships can be written as:
V=V1=V2=V3=...V=V1=V2=V3=...
I=I1+I2+I3+...I=I1+I2+I3+...
1Req−parallel=1R1+1R2+1R3+...1Req−parallel=1R1+1R2+1R3+...
NOTE: If you have already studied capacitors and therules for finding the equivalent capacitance, you should noticethat the rules for the capacitors are similar - but not quite thesame as the ones discussed here.In this problem, you will use the the equivalent resistanceformulas to determine ReqReqR_eq for various combinationsof resistors.
1 of 4The figure represents three resistors, labeled as R 1, R2, and R 3, connected in series from left to right. There is acurrent I flowing from left to right through them.
Part A
Part complete
For the combination of resistors shown, find the equivalentresistance between points A and B.(Figure 3)
Express your answer in Ohms.
--
SubmitPrevious AnswersRequest Answer
Part B
Part complete
For the set-up shown, find the equivalent resistance betweenpoints A and B.(Figure 4)
Express your answer in Ohms.
--
nothing