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 resistors

Complex Circuit Networks Combination of series and parallel To analyze, first find total resistance (R T ), then total current To simplify resistance networks, replace several resistances with one equivalent resistance(R eq ) 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