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## PowerPoint Slideshow about 'Series and Parallel Elements' - oistin

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### Series and Parallel Elements

Equivalent Resistance

Series and Parallel Elements

- Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current through them.
- Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

Series Resistors

- The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.

Voltage Division

- To determine the voltage across each resistor we use:
- The voltage is divided among the resistors in direct proportion to their resistances.

Parallel Resistors

- The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum.

Parallel Resistors (cont.)

- The equivalent resistance of N resistors in parallel is
- Req is always smaller than the resistance of the smallest resistor in the parallel combination.
- If the resistances are equal, simply divide by the number of resistors.

Parallel Conductance

- It is often more convenient to use conductance when dealing with parallel resistors.
- The equivalent conductance of resistors connected in parallel is the sum of their individual conductances.

Serial Conductance

- The equivalent conductance of series resistors is obtained in the same manner as the resistance of resistors in parallel.

Current Division

- For two resistors in parallel, the resistors will have current

Current Division (cont.)

- The total current i is shared by the resistors in inverse proportion to their resistances.
- If a current divider has N conductors in parallel, the nth conductor (Gn) will have current

Examples

- Find Req by combining the resistors.

Examples

- Calculate the equivalent resistance Rab in the circuit.

Examples

- Find the equivalent conductance Geq for the circuit.

Examples

- Find the currents and voltages in the circuit.

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