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Physics
Maths
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The name derives from the shapes of the circuit diagrams
The Y-Δ transform, also written Y-delta, Wye-delta, Kennelly’s delta-star transformation, star-mesh transformation, T-Π or T-pi transform, is a mathematical technique to simplify the analysis of an electrical network.
The transformation is used to establish equivalence for networks with 3 terminals. Where three elements terminate at a common node and none are sources, the node is eliminated by transforming the impedances. For equivalence, the impedance between any pair of terminals must be the same for both networks. The equations given here are valid for real as well as complex impedances.
Given “g” be the function defined on the set of all real numbers by g(x)=1, If x is rational and g(x)=exp(x) , if x is irrational,Now, at x = 0 since 0 is rational number g(x) =1 At h tending to 0 or h--->0,Now RHL = Lim h--->0 g(0+h)there are two possibilitiesa) either h = rational, if so, Lim h--->0 g(0+h) = 1b) or h = irrational, then Lim h--->0 g(0+h) = exp (h) = exp (0) = 1Similarly we can prove that Left hand limit, LHL = Lim h--->0 g(0-h) = 1thus we see that, RHL = LHLHence g(x) is continuous at 0.
Given “g” be the function defined on the set of all real numbers by g(x)=1, If x is rational and g(x)=exp(x) , if x is irrational,
Now, at x = 0 since 0 is rational number g(x) =1
At h tending to 0 or h--->0,
Now RHL = Lim h--->0 g(0+h)
there are two possibilities
a) either h = rational, if so, Lim h--->0 g(0+h) = 1
b) or h = irrational, then Lim h--->0 g(0+h) = exp (h) = exp (0) = 1
Similarly we can prove that Left hand limit, LHL = Lim h--->0 g(0-h) = 1
thus we see that, RHL = LHL
Hence g(x) is continuous at 0.
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