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 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 R T = R 1 + R 2 + R 3 + … 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 Resistor V = IR For a capacitor V = Q/C For multiple capacitors in series the total capacitance is 1/C = 1/C 1 + 1/C 2 + 1/C 3 + …

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/R T = 1/R 1 + 1/R 2 + 1/R 3 + … The total resistance for a parallel circuit is smaller than any of the individual resistors. Capacitors in a parallel circuit: C = C 1 + C 2 + C 3 + …

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 (I 1, I 2, I 3 …) 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 = I 2 R P = V 2 /R