Water Analogy

A simple electrical circuit - consisting of a battery and a resistor - can be modeled by a pump to simulate a battery and a paddle to simulate electrical resistance.

As the current turns the paddle it does work and thus loses some energy similar to electrical current flowing through a resistor.

Simple Circuit

Series Circuits

Only one path for circuit current Current the same in all parts of

circuit Sum of voltage drops across circuit

elements equals battery voltage Total circuit resistance equals sum

of separate resistances

Series Circuit

Parallel Circuits

More than one conducting path for circuit current

Two or more components connected across two common points in circuit

Currents in parallel branches vary inversely with branch resistance; total current = sum of branch currents

Parallel Circuits

Voltage drop the same across parallel branches

Parallel resistances add following reciprocal rule: reciprocal of total resistance equals sum of reciprocals of individual resistances

Parallel Circuit

Adding Parallel Resistances For two parallel resistors

For two or more parallel resistors21

21

RR

RRReq

...1111

321

RRRReq

Complex Circuit Networks

Combination of series and parallel To analyze, first find total

resistance (RT), then total current To simplify resistance networks,

replace several resistances with one equivalent resistance(Req)

Start with series resistances and combine

Complex Circuit

Then collapse parallel branches into one equivalent resistance

Combine series resistances created by previous step

Continue until only one equivalent resistance remains

Complex Circuit

Kirchhoff’s Rules

Algebraic sum of currents at any circuit junction equals zero; or currents into a junction equal currents leaving the junction; conservation of charge

Algebraic sum of all voltage drops around a circuit loop equals zero; conservation of energy

Overload Protection Homes have 120 volt lines from

power company Home circuits are connected in

parallel Each parallel branch lowers total

resistance, increasing current in supply lines

Overload Protection Lines can become overloaded

causing heating and fire danger Circuits protected by fuses or

circuit breakers which open circuit if current rises beyond certain value

Protect against short circuits where bare wires touch together

Battery Cells

Wet cells: use liquid electrolyte - car battery

Dry cells: use paste “dry” electrolyte - flashlight batteries

Primary cells: replaced when reactants are used up

Storage cells: easily recharged Fuel cells: New reactants added as

needed

Combinations of Cells

Battery is combination of cells connected in series, parallel, or combination of both

Cells in series: cells connected + to -, as in a flashlight

battery voltage = sum of cell voltages; battery current = current of one cell, the same throughout; battery resistance = sum of cell resistances

Combinations of Cells

Cells in parallel: - terminals all connected together and + terminals all connected together

Battery voltage = voltage of one cell; total current drawn by circuit is divided equally among the cells; battery resistance is reciprocal of the sum of reciprocals of cell resistances

Electrical Measurements

Voltmeter must be placed in parallel with circuit element whose voltage drop is being measured

Ammeter must be placed in series so that all circuit current flows through ammeter.

Never connect the ammeter in parallel like the voltmeter

Measuring Resistance Resistance can be measured using a

voltmeter and ammeter and calculating resistance using Ohm’s Law

Some error is introduced by the meters Multimeter uses this method Wheatstone bridge gives more precise

measurement