Electric Current and Circuits

Ch. 18

Electric Current

• A net flow of charge• Variable = I• Unit = Ampere (A)• I = Δq/Δt• Conventional current is the direction a positive

charge would flow

Potential Difference

• Just like a ball will not fall if there is not a difference in gravitational potential, an electron would not move (ie no current generated) if there is not a difference in electric potential

• To have a current, you need a potential difference.

EMF

• Potential difference maintained by an ideal battery

• EMF is measured in volts (V)• Measure of the work done by the battery per

unit of charge

• W = Ԑq

Current, Water, and Batteries

• Water runs down an incline passing through a

water wheel. When the water is at the

bottom, a person carries the water back up to

the top.

resistor

current

current

battery current

Batteries and Voltage

• A 9V battery keeps a positive terminal that is 9V higher in potential difference than the negative terminal.

• The battery does 9 J of work for every C it pumps through. The battery does work by converting stored chemical energy into electric energy.

More about Batteries

• Batteries come in different EMFs (voltages) (1.5V, 6V, 9V, etc) and different sizes (AAA, AA, C, D…)

• The common batteries all have 1.5V. This means a larger batter can last longer or supply charge faster than a smaller one.

Types of Currents

• Direct Current– The current in any branch always moves in the

same direction• Alternating Current– The currents periodically reverse directions.

Electrons and Current

• Since current was defined (by Albert Einstein) to be the direction a positive charge would flow…

• Electrons move in the direction opposite the current.

Resistance

• The current (I) that flows through a conductor is proportional to the potential difference (ΔV) that supplies it. (Ohm’s Law)

• Some materials allow current to flow more freely than others. A measure of how well the current flows is called resistance.

• R = ΔV/I• Or more commonly… V = IR• Resistance is measured in ohms (Ω)

Resistance of Materials

• R = ρL/A

• Long wires provide more resistance than short wires

• Skinny wires provide more resistance than fat wires

• When in doubt, think of a water hose.

Superconductors

• Materials with a resistivity approaching zero when cooled to a very low temperature (close to absolute zero)

• Resistance also increases when the temperature increases.

Resistors

• In a circuit, resistors are materials that cause a drop in voltage

• Typically the resistance is known

Kirchhoff’s Rules

• At a junction, the current entering the junction is equal to the current leaving a junction.

• The net voltage drop around a circuit is zero. All the potential created by the battery must be used up by the resistors.

Series Circuits

• The same current flows through each resistor

Series Circuits

• The total resistance in a series circuit is a sum of all the individual resistors connected in series

• RT = R1 + R2 + R3 + … • The total resistance is larger than any of the

individual resistances

Series Circuits

• Things that are connected in series have the same current, but different voltages (unless they have the same resistance)

Series Circuits

• For a ResistorV = IR

• For a capacitorV = Q/C

• For multiple capacitors in series the total capacitance is

• 1/C = 1/C1 + 1/C2 + 1/C3 + …

Parallel Circuits

• Resistors are wired so that the potential difference across them is the same.

Parallel Circuits

• Things that are connected in parallel have the same voltages, but different currents (unless they have the same resistance).

• Benefits to parallel circuits…– When one light bulb goes out, the current still has

a path to travel through so the other light bulbs stay lit.

Parallel Circuits

• 1/RT = 1/R1 + 1/R2 + 1/R3 + …

• The total resistance for a parallel circuit is smaller than any of the individual resistors.

• Capacitors in a parallel circuit:C = C1 + C2 + C3 + …

Drawing Circuits

• Things you must have…– Battery – long side is the positive terminal and

short side is negative terminal. The current leaves the positive end.

– Wire– Resistor – Drawn as zig zag lines, not light bulbs.

Each resistor must be labeled.– Switch – to open or close the circuit (not always

necessary)

Solving Circuit Problems

• Simplify the resistors• Assign variables to the current in each branch (I1, I2,

I3…) and choose a direction for each. Draw the circuit with the current flow indicated by arrows.

• Apply the Junction Rule• Apply the loop rule– If your loop goes against the current in a resistor, V is +. If

your loop goes with the current, V is – – If your loop goes from – to + terminal in a battery, the

voltage is +. From + to – is a negative voltage.

Electric Power

• P = IV• P = I2R• P = V2/R