Series - Parallel Circuits EE 2010: Fundamentals of Electric Circuits Mujahed AlDhaifallah

Definition Series – Parallel circuits are networks that contain both series and parallel circuit configurations.

General Approach for Solving Take a moment, before you start calculating.  The answer may be a lot simpler than reducing everything.  There may be many “time” and “energy” saving shortcuts to solve the problem. Examine each region independently, before tying them together.

Reduce and Return Approach Applicable to all single source circuits.

Example

Ladder Networks

There are 2 approaches to solve this circuit  Reduce Resistances using series parallel analysis  Assign a letter symbol to the last branch current and work back through the network to the source, maintaining this assigned current or other current of interest

Ladder Networks Reduce Resistances??  That’s easy!!!

Ladder Networks Assign a letter symbol to the last branch current and work back through the network to the source Let’s do it!!!

Voltage Divider Supply What should I do if I want multiple voltage outputs from the same 120V battery?

Voltage Divider Supply R1R1 R2R2 R3R3 V3V3 V2V2 V1V1

What’s the value of V1, V2 and V3? 120V = V 1 > V 2 > V 3 V1V1 V2V2 V3V3

Voltage Divider Supply We cannot calculate V 2 and V 3 unless we know what load is connected to them The less the load, the closer they are to 120V. V1V1 V2V2 V3V3

No - Load When is “no load” observed?  When R 2 is infinitely large?  Or when R 2 is zero? R1R1 R2R2

No - Load When is “no load” observed?  When R 2 is infinitely large?  Or when R 2 is zero? When R 2 is infinite!!! R1R1 R2R2

Example

Continue If the load resistors are changed to the 1-k ohm level what will happen? the terminal voltages will all be relatively close to the no-load values. If we compare current drains established by the applied loads, we find for network 1

Potentiometer

Voltage Sources Two voltage sources of different ratings may not be connected in parallel. Why? Series operation, however, is permitted.

Current Sources Two current sources of different rating may not be connected in series. Parallel operation, however, is permitted.