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how can nodal analysis, the plucking method and the star delta method be justified....i can't find the derivations of these methods anywhere.....i want to know how they work....i also want to know how equipotential points are determined......
7 years ago
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Nodal Analysis of Electric Circuits In this method, we set up and solve a system of equations in which the unknowns are the voltages at the principal nodes of the circuit. From these nodal voltages the currents in the various branches of the circuit are easily determined. The steps in the nodal analysis method are:
In this method, we set up and solve a system of equations in which the unknowns are the voltages at the principal nodes of the circuit. From these nodal voltages the currents in the various branches of the circuit are easily determined. The steps in the nodal analysis method are:
I_{a} + I_{b} + I_{c} = 0
Compare the resistances between terminals 1 and 2.
Resistance between the terminals 2 and 3.
Resistance between the terminals 1 and 3.
This now gives us three equations and taking equation 3 from equation 2 gives:
Then, re-writing Equation 1 will give us:
Adding together equation 1 and the result above of equation 3 minus equation 2 gives:
From which gives us the final equation for resistor P as:
Then to summarize a little the above maths, we can now say that resistor P in a Star network can be found as Equation 1 plus (Equation 3 minus Equation 2) or Eq1 + (Eq3 - Eq2).
Similarly, to find resistor Q in a Star network, is equation 2 plus the result of equation 1 minus equation 3 or Eq2 + (Eq1 - Eq3) and this gives us the transformation of Q as:
And again, to find resistor R in a Star network, is equation 3 plus the result of equation 2 minus equation 1 or Eq3 + (Eq2 - Eq1) and this gives us the transformation of R as:
When converting a Delta network into a Star network the denominators of all of the transformation formulas are the same: A + B + C, and which is the sum of ALL the Delta resistances. Then to convert any Delta connected network to an equivalent Star network we can summarized the above transformation equations as:
The value of the resistor on any one side of the Delta, Δ network is the sum of all the two-product combinations of resistors in the Star network divide by the Star resistor located "directly opposite" the Delta resistor being found. For example, resistor A is given as:
with respect to terminal 3 and resistor B is given as:
with respect to terminal 2 with resistor C given as:
with respect to terminal 1.
By dividing out each equation by the value of the denominator we end up with three separate transformation formulas that can be used to convert any Delta resistive network into an equivalent Star network as given below.
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