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Understanding DC Resistive Circuits: Methods & Laws | Circuit Analysis Example

Learn about resistors in series and parallel circuits, solving circuits using substitution, Kirchhoff’s laws application tips with examples.

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Understanding DC Resistive Circuits: Methods & Laws | Circuit Analysis Example

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  1. CH 20-3

  2. 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.

  3. Example If the resistors below are light bulbs, rank the bulbs in terms of brightness. 3 V 5  10  5 

  4. 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.

  5. Example What is the current through each resistor and the voltage across each resistor in the circuit below? 10  3 V 60  30  30 

  6. The Current Law (or Node Ruleor Junction Rule) Conservation of charge -- the current into a node is equal to the current out of the node.

  7. The Voltage Law (or Loop Rule) Conservation of Energy -- The voltage around a closed loop is zero.

  8. Tips for applying Kirchhoff’s Laws Define all resistors and batteries. Define currents going through each element. At each node, apply Kirchhoff’s Current Law. Sketch closed loops. 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.) Solve simultaneous equations for all unknowns.

  9. Example What is the current through each resistor and the voltage across each resistor in the circuit below? 10  9 V 20  30  3 V

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