lecture 03_parallel circuit

8/20/2019 Lecture 03_Parallel Circuit

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Parallel Circuit

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Series or Parallel???

Comment on whether R1, R2 and R3 are in series/parallel/series-parallel

combination. Signify your answer.

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Parallel elementsTwo elements, branches, or networks are in parallel if they have

two points in common.

FIG. 1 Different ways in which three parallel elements may appear.

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Total conductance & resistance

Recall that for series resistors, the total resistance is the sum of the

resistor values. What about conductance???

Can you work it out?????

For parallel elements, the total conductance is the sum of the individual

conductances.

That is, for the parallel network

of Fig. 2, we write

FIG. 2 Determining the total conductance of

parallel conductances.

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Total conductance & resistance

Substituting resistor values for the network of Fig. 2 will result inthe network of Fig. 3. Since G =1/R , the total resistance for the network

can be determined by direct substitution into the equation of GT ,

FIG. 3 Determining the total resistance of

parallel resistors

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Example problemsQ.1 Find the total resistance for the circuit shown in fig 4.

Also find the total conductance.

FIG. 4 Circuit diagram for example problem#1

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Resistors in parallel…….

The total resistance of parallel resistors is always less than the value

of the smallest resistor. (check it out with Q.1 u just did!!!)

For equal resistors in parallel, the equation becomes significantly easier

to apply. In other words, the total resistance of N parallel resistors of

equal value is the resistance of one resistor divided by the number (N)

of parallel elements.

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Resistors in parallel……. The total resistance of two parallel resistors is the product of the two

divided by their sum.

Parallel elements can be interchanged without changing the

total resistance or input current.

For parallel resistors, the total resistance will always decrease as

additional elements are added in parallel.

For 3 parallel resistors

Q.2 Find the RT for the circuit in fig. 5.

FIG. 5 Circuit diagram for

example problem#2 8M.S.Muhit


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Resistors in parallel…….

The voltage across parallel elements is the same.

FIG. 6 Parallel network.

For single-source parallel networks, the source current (I s ) is equal

to the sum of the individual branch currents.

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Example problemsQ.3 For the parallel network of Fig. 7

a. Calculate RT .b. Determine Is.

c. Calculate I1 and I2, and demonstrate that Is = I1+I2.

d. Determine the power to each resistive load.

e. Determine the power delivered by the source, and compare it to the

total power dissipated by the resistive elements.


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Example problemsQ.4 Given the information provided in Fig. 8,

a. Determine R3.b. Calculate E.

c. Find Is.

d. Find I2.

e. Determine P2.


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Don’t use calculator……… Q.5 Determine the currents I1 ,I3 ,I4 & I5 of Fig. 9 using Kirchhoff’s

current law.


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Don’t use calculator………

Q.6 Find the magnitude and direction of the currents I3 , I4 , I6 , and I7 for

the network of Fig. 10. Even though the elements are not in series or

parallel, Kirchhoff’s current law can be applied to determine all the

unknown currents.


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Current divider ruleFor two parallel elements of equal value, the current will divide equally.

For parallel elements with different values, the smaller the resistance, thegreater the share of input current.

For parallel elements of different values, the current will split with a ratio

equal to the inverse of their resistor values.

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Current divider rule

Technique #2

Current seeks the path of least resistance. 16M.S.Muhit


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Voltage sources in parallel

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Open circuit

An open circuit can have a potential difference ( voltage ) across its

terminals, but the current is always zero amperes.

FIG. 11 Demonstrating the characteristics of an

open circuit.

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Short circuit A short circuit can carry a current of a level determined by the external

circuit, but the potential difference (voltage) across its terminals is always zero volts.

Net resistance = 0; V=10 V, hence, I=infinite.

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FIG. 12 Single phase of house wiring:

physical details ;

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Reference

1. Introductory Circuit Analysis by Robert . L. Boylestad

2. http://www.electronics-tutorials.ws/dccircuits/dcp_1.html

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lecture 03_parallel circuit

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