Three resistors with resistances R1 = 55.0 ?, R2 = 91.0 ? and R3 = 38.0 ? are pl

Question

Three resistors with resistances R1 = 55.0 ?, R2 = 91.0 ? and R3 = 38.0 ? are placed along the sides of a triangle as shown in circuit 1. What are the values of the resistances Ra, Rb and Rc that would provide an equivalent circuit as arranged in circuit 2?

Three resistors with resistances R,-55.0 , R2-91.0 and R3-38.0 are placed along the sides of a triangle as shown in circuit 1. What are the values of the resistances Ra, Rb and Re that would provide arn equivalent circuit as arranged in circuit 2? Number Number R. R.= Ra Number Circuit 1 Circuit Circuit 2

Explanation / Answer

given data

resistances R1 = 55.0 , R2 = 91.0 and R3 = 38.0

Actually we know that

when resistors in series

Requivalent in series = R1 + R2 + R3

when resistors in paralel
1/Requivalent in parallel = 1/R1 + 1/R2 + 1/R3

R1 + R2 + R3 =55+9

Ra = [R1 x R3]/[R1 + R2 + R3]

Ra = (55*38)/(184) = 11.35 ohm

Rb = [R1 x R2]/[R1 + R2 + R3]

=55*91/184 = 27.20 ohm

Rc = [R2 x R3]/[R1 + R2 + R3]
=91*38/184 = 18.79 ohm

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