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Resistors in Parallel

Resistors in Parallel. Resistors connected at a single node pair Voltage across each resistor is the same. 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. Apply KCL and Ohm’s Law.

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Resistors in Parallel

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

  2. Caution on Parallel Connection • Here, R1 and R3 are not in parallel • Resistor R1 is in parallel with the series combination of R2 and R3 ECE 201 Circuit Theory I

  3. Apply KCL and Ohm’s Law i1 i2 i3 i4 ECE 201 Circuit Theory I

  4. Solving for each current ECE 201 Circuit Theory I

  5. Substitute back ECE 201 Circuit Theory I

  6. Equivalent Circuit ECE 201 Circuit Theory I

  7. Special case for only 2 resistors Product Sum ECE 201 Circuit Theory I

  8. 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 ECE 201 Circuit Theory I

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