Lecture 5 Review Series parallel circuit elements Circuit

Lecture 5 • Review: • Series, parallel circuit elements • Circuit reduction • Related educational modules: –Section 1. 5

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: -V 1 + i·R 1 + V 2 + i·R 3 – V 3 + i·R 4 = 0 (-V 1 + V 2– V 3) + i(R 1 + R 2 + R 3 + R 4) = 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 20 V source

Voltage Division • Series combination of N resistors:

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 V 1 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 2 A source

Current Division • Parallel combination of N resistors:

Current Divider Formula • Ratio of i. K 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 = 2 m. A

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. )