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Parallel Circuits ENTC 210: Circuit Analysis I Rohit Singhal Lecturer Texas A&M University

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Are these resistors in Parallel?

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Parallel Elements Two Elements, branches or networks are in parallel if they have two points in common.

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Resistance Resistance is inversely proportional to the cross sectional area direction of current flow

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Resistance Resistance is inversely proportional to the cross sectional area direction of current flow

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Resistance R = ρ L/(A 1 +A 2 ) Solving in terms of R1 and R2 gives 1/R = 1/R 1 + 1/R 2 The total value of the resistance is always smaller than the smallest resistance

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Resistance, etc. The total resistance will decrease with each new added parallel branch The voltage across each resistor is the same The total current is the sum of all the branches The total power dissipated is the sum of power dissipated in all resistors.

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Kirchhoff’s Current Law KCL states that the algebraic sum of the currents entering and leaving a point or junction is zero. i 1 +i 2 +i 3 +i 4 =0 i1i1 i2i2 i3i3 i4i4

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Current Divider Rule For parallel elements of different value the current will split with a ratio equal to the inverse of their resistor value

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