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ECE 201 Circuit Theory I1 Resistors in Parallel Resistors connected at a single node pair Voltage across each resistor is the same

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ECE 201 Circuit Theory I2 Caution on Parallel Connection Here, R 1 and R 3 are not in parallel Resistor R 1 is in parallel with the series combination of R 2 and R 3

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ECE 201 Circuit Theory I3 Apply KCL and Ohm’s Law i 1 i 2 i 3 i 4

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ECE 201 Circuit Theory I4 Solving for each current

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ECE 201 Circuit Theory I5 Substitute back

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ECE 201 Circuit Theory I6 Equivalent Circuit

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ECE 201 Circuit Theory I7 Special case for only 2 resistors Product Sum

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ECE 201 Circuit Theory I8 Summary Resistors in parallel have the same voltage The resistors can be replaced by an “equivalent” resistance whose conductance is the sum of the individual conductances The “equivalent” resistor is smaller than the smallest of the individual resistors

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