Series/Parallel Circuits

Section 3.1-3.4

Concepts Studied So Far

• Ohm’s Law: Victory Is Rare • Power: P=IV • KCL• KVL

Outline

• Resistors in Series→ Req• Resistors in Parallel → Req• Voltage Divider Circuits →Voltage

divider formula• Current Divider Circuits →Current

divider formula

Resistors Connected in Series

Series-connected circuit elements carry the same current

Equivalent Resistor

Req=R1+R2+R3

….

Exercise

Identify the resistors connected in series

Resistors in Parallel

• Parallel-connected circuit elements have the same voltage across their terminals

Equivalent Parallel Resistor

1/Req=1/R1+1/R2+1/R3+1/R4

Series Parallel Simplification

P3.5

Find Rab

P3.7

Find Rab

The Voltage-Divider Circuit

Function: to develop more than one voltage level from a single voltage supply

A Voltage Divider Connected to a Load

The Current Divider Circuit

Example 3.3

Calculate power dissipated in the 6 Ohm resistor

Problem 3.14

vo(no load)=4 Vvo(load)=3 VFind RL

3.15

Assume that only 0.5 W resistors are availableThe no-load voltage is to be the same as in the schematic. Specify the smallest values of R1 and R2

Application: Photovoltaic System

• Solar Cell– I-V Characteristics Equation–Series construction–Parallel construction

I-V Characteristics of a Solar Cell

Open Circuit Voltage (Voc)

Short CircuitCurrent I(Isc)

I-V Characteristics shows all the possible operating pointfor the solar panel

Open Circuit Voltage Measurement

Observation: there is no current at Voc.

Short Circuit Current Measurement

Why is OK to short circuit a solar cell?

It is possible to produce short circuit a solar panel becauseThe current comes from the electrons produced by the solar cell. Only some of the photons striking the solar cellare converted into current. The current produced by the solar cell is finite.

Power Produced by Solar Cell

P=IVObservation: No power is produced atVoc and Isc. Why?

Example

If Vmp is 15 V and Imp is 3A, what resistance is requiredin order to operate the solar cell at its maximum power?

Answer: A 5 Ohm load.

Rule of Thumb

• Solar cells are generally connected in series to achieve a desired voltage.

• The serial connected solar cells are connected in parallel to build current and power.

• Cells are connected to form modules and modules are connected to form array.

Connect Cells/Modules in Series

Individual cells are connected in series by soldering the metal stripfrom top surface (- terminal) of one cell to the back surface (+ terminal)of the next

Use Series Connection to Increase Voltage

You want to use cells of matching current capacity!

Use Parallel Construction to Increase Current

(Acquire proper voltage)

Increase Current Capacityby Connecting Cells in Paralell