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
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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