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Lecture 5 •Review: •Series, parallel circuit elements •Circuit reduction •Related educational materials: –Chapter 2.1, 2.2, 2.3 Review: series and parallel circuit elements • Elements in series if they have the same current • Elements in parallel have the same voltage Circuit reduction • Some circuit problems can be simplified by combining elements to reduce the number of elements • Reducing the number of elements reduces the number of unknowns and thus the number of equations which must be written to determine these unknowns Series circuit elements – example 1 • Apply KCL at any node all elements have the same current • All of the above circuit elements are in series Series element circuit reduction – example 1 • KVL around the loop: -V1 + i·R1 + V2 + i·R2 + i·R3 – V3 + i·R4 = 0 (-V1 + V2– V3) + i(R1 + R2 + R3 + R4) = 0 Series circuit reduction • Notes: • Voltage sources in series add directly to form an equivalent voltage source • Resistances in series add directly to form an equivalent resistance Series circuit reduction – Example 2 • Determine the power delivered by the 20V source Voltage Division • Series combination of N resistors: i + Vk - Voltage Divider Formula • Ratio of VK to the total voltage is the same as the ratio of RK to the total series resistance Voltage Dividers – special case • Voltage source in series with two resistors: Voltage division – example 1 • Determine the power dissipated by the 2 resistor Voltage division – example 2 • Determine the voltage V1 in the circuit below. Parallel circuit elements – example 1 • Apply KVL around any loop all elements have the same voltage • All of the above circuit elements are in parallel Parallel element circuit reduction – example 1 • KCL at upper node: Parallel circuit reduction • Notes: • Current sources in parallel add directly to form an equivalent current source • Definition: Conductance is the inverse of resistance • Units are siemens or mhos (abbreviated S or ) • Conductances in parallel add directly to form an equivalent conductance • Go back to previous example, look at it in terms of conductances Parallel element circuit example 1 – revisted Parallel circuit reduction – Example 2 • Determine the power delivered by the 2A source Current Division • Parallel combination of N resistors: Current Divider Formula • Ratio of iK to the total current is the same as the ratio of GK to the total parallel conductance Current Divider – special case • Current source in parallel with two resistors Current division – example 1 • Determine the current in the 2 resistor Current division – example 2 • Determine the value of R which makes i = 2mA Circuit Reduction • Series and parallel combinations of circuit elements can be combined into a “equivalent” elements • The resulting simplified circuit can often be analyzed more easily than the original circuit Circuit Reduction – example 1 • Determine the current in the 2 resistor. (Note: we wrote the governing equations for this example in lecture 3.)