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CH 20-3
Review
Series resistors have the same current; the total voltage
is “divided” across the resistors.
Parallel resistors have the same voltage; the current
splits so that part of the current flows through one resistor
and the other part of the current flows through the other
resistor.
Example
If the resistors below are light bulbs, rank the bulbs in
terms of brightness.
3V
5
10 
5
Solving DC Resistive Circuits:
Method of Substitution
This method is most effective when there is one
battery.
1. Combine series resistors and parallel resistors into
their equivalent resistance.
2. Find the current through the battery.
3. Expand the equivalent resistance into the
individual resistors.
4. Calculate the current through each resistor and
voltage across each resistor.
Example
What is the current through each resistor and the voltage
across each resistor in the circuit below?
10 
60 
3V
30 
30 
The Current Law (or Node Rule
or Junction Rule)
Conservation of charge -- the current into a node is
equal to the current out of the node.
The Voltage Law (or Loop Rule)
Conservation of Energy -- The voltage around a
closed loop is zero.
Tips for applying Kirchhoff’s Laws
1. Define all resistors and batteries.
2. Define currents going through each element.
3. At each node, apply Kirchhoff’s Current Law.
4. Sketch closed loops.
5. Apply Kirchhoff’s Voltage Law for each loop. Use passive
convention -- As you go around a closed loop, if you go in the
direction of current through a resistor, then it is a positive
voltage (opposite the current is a negative voltage). As you go
around a closed loop, if you first encounter the  terminal of a
battery, then it is a negative voltage across the battery (if the +
terminal, then it is a positive voltage.)
6. Solve simultaneous equations for all unknowns.
Example
What is the current through each resistor and the voltage
across each resistor in the circuit below?
10 
3V
9V
20 
30 