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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