Power Input to a Source Current flows “backwards” Work is being done on, rather than by the top battery (source of non-electrostatic force) Rate of conversion of electric energy into non-electrical energy

Circuits in Series Resistance (light bulbs) on same path Current has one pathway - same in every part of the circuit Total resistance is sum of individual resistances along path Current in circuit equal to voltage supplied divided by total resistance Sum of voltages across each lamp equal to total voltage One bulb burns out - circuit broken - other lamps will not light (think of string of old Christmas lights)

ISNS Phenomena of Nature Water Analogy for Series Circuits

Resistors in series

Parallel Circuits Bulbs connected to same two points of electrical circuit Voltage same across each bulb Total current divides among the parallel branches - equals sum of current in each branch - current in each branch inversely proportional to resistance of branch Overall resistance of circuit lowered with each additional branch Household wiring (and new Christmas light strings) designed in parallel - too many electrical devices on - too much current - trip fuse/breaker

ISNS Phenomena of Nature Water Analogy for Parallel Circuits

Resistors in parallel

Calculating resistance A variable cross-section resistor treated as a serial combination of small straight-wire resistors:

Example: Equivalent resistances

Series versus parallel connection What about power delivered to each bulb? What if one bulb burns out?

Symmetry considerations to calculate equivalent resistances No current through the resistor I1I1 I1I1 I1I1 I1I1 I1I1 I1I1 I2I2 I2I2 I2I2 I2I2 I2I2 I2I2

Kirchhoff’s rules To analyze more complex (steady-state) circuits: 1.For any junction: Sum of incoming currents equals to sum of outgoing currents (conservation of charge) Valid for any junction 2.For any closed circuit loop: Sum of the voltages across all elements of the loop is zero (conservation of energy) Valid for any close loop - The number of independent equations will be equal to the number of unknown currents Loop rule – statement that the electrostatic force is conservative.

Sign conventions for the loop rule

A single-loop circuit Charging of a car battery

Complex networks Find currents, potential differences and equivalent resistance

Electrical Measuring Instruments Galvanometer Can be calibrated to measure current (or voltage) Example: Full-scale deflection I fs =1 mA, internal coil resistance R c =20 

For max current reading I a of 50mA For max voltage reading V v =10V