Question

2012 Calculate the final equivalent resistance between terminals A and B? Ensure that you draw out each step. You should follow the process: a. Identify the parallel resistors using their labels and the parallel symbol notation (e.g. Rx = R1 || Rs), then work out the equivalent values for the parallel resistance(s), using your designated labels (e.g. Rx = 492). b. Redraw the circuit with the parallel resistors replaced by their equivalent resistance(s). Hint: replacing parallel resistors does not remove any nodes! c. Redraw the circuit with the series resistors replaced by their equivalent resistance(s). Note: replacing series resistors removes nodes! d. Repeat steps (a)-(d) as many times as necessary to reduce the network to a single resistance of Req. Reg =

Answer 1

Solution :
Branch Contains a single electrical element like voltage/current source or, resistor/inductor/capacitor e.t.c.

Here, in the figure there are 10 resistors,

[Branches are marked in RED.]

So,Number of branch = 10.

Nodes are points where, two or more branches joints.

[Nodes are labeled as N1,N2,N3.,N4,N5]

[D and H are Same node]

So, Number of Nodes = 5.

A loop is a any closed path in a circuit.

Loops Can be found by this formula.

Loops = Branch - Node + 1

Here, AC and BD are open and not a part of loop. So,Number of branch which is part of loop is, 8.

Loops = 8 - 5 + 1 = 4 .

Find out Equivalent Resistance.

Let's Assume this circuit.

Here,

CE and EF are in series, Equivalent,Rx1 = 4+4 = 8 ohm.

FG and GH are in series, Equivalent,Rx2 = 20+4 = 24 ohm.

Rx1 and R10 are parallel , So, Equvalent,Rx3 = (Rx1*R10)/(Rx1+R10) = 8*8/(8+8) = 64/16 = 4 Ohm.

R3,R11 and Rx2 are in parallel, So,Equivalent,Rx4

= (1/R3 + 1/R11 + 1/Rx2)^-1 = ( 1/12 +1/8 +1/24 )^-1 = 4 ohm.

Rx3 and Rx4 are in series,Equivalent Rx5 = 4+4 = 8 ohm

Rx5 and R6 are parallel, Equivalent, Rx6 = (1/8+1/2)^-1 = 1.6 ohm

Now, R8 ,Rx6 and R9 are in series.

So, Equivalent resistance between A,B is R_AB 3+1.6+3 = 7.6 ohms.

Hope I make it clear to understand.

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