AP Physics C: E&M

DC: Direct current. A constantly applied voltage causes charged particles to drift in one direction

+-+- Voltage source C1C1 C2C2 C3C3 Adding capacitors in series will lower the capacitance of the circuit when compared to the possible capacitance of just one capacitor in the circuit. Only the first plate of the first capacitor and the last plate of the last capacitor are actually connected to the voltage source, so only these plates will gain or lose electrons due to the potential difference of the battery.

+-+- Voltage source C1C1 C2C2 C3C3 The inner plates are induced with charge. All capacitors carry an equivalent charge Q. The voltage across all elements in the series will add up to that of the battery. Each capacitor has a different capacitance and has the same charge, so the individual voltages will differ.

+-+- Voltage source C1C1 C2C2 C3C3 This should not be surprising since you are basically just making one big capacitor with a larger separation (d). Q is the same for all so the equivalent capacitance can be found with:

+-+- Voltage source C1C1 Adding capacitors in parallel will raise the capacitance of the circuit when compared to the possible capacitance of just one capacitor in the circuit. All capacitors are directly connected to the same voltage source so they will each reach the same potential difference when charged. C2C2 C3C3

Since each capacitor may have a different capacitance, each may hold a different amount of charge, but the sum of the charge will equal that of one capacitor to replace those in parallel Voltage source C1C1 C2C2 C3C3

This should not be surprising since you are basically just making one big capacitor with a larger surface area (A) for charge to be stored. V is the same for all so the equivalent capacitance can be found with: +-+- Voltage source C1C1 C2C2 C3C3

A +-+- B C +-+- DE

It takes over 6.24 billion billion electrons to add up to one coulomb! 1 C of charge through any cross section of wire per second is one AMP! Electric current is the amount of charge passing through a certain area per second. It is measured in amperes.

If the charge flow rate varies, we define the instantaneous current as: The direction of current is the direction that positive charges would flow if free to do so. n=number of charge carriers per unit volume A=cross-sectional area of wire Δx=length of section of wire ΔQ=charge in a section of wire q=charge on each particle n=number of charge carriers per unit volume A=cross-sectional area of wire Δx=length of section of wire ΔQ=charge in a section of wire q=charge on each particle

If charge carriers move with a velocity v d, then they move a distance Δx=v d Δt If charge carriers move with a velocity v d, then they move a distance Δx=v d Δt

With no voltage, charges in a metal bounce around randomly similar to gas molecules. With a voltage they still bounce around but slowly drift in one direction.

A copper wire with cross-sectional area3x10 -6 m 2 carries a current of 10.0A. Find the drift speed of the electrons. The density of copper is 8.95g/cm 3. from the periodic table atomic mass of copper: m=63.5g/mol from the periodic table atomic mass of copper: m=63.5g/mol

A copper wire with cross-sectional area3x10 -6 m 2 carries a current of 10.0A. Find the drift speed of the electrons. The density of copper is 8.95g/cm 3.

 We will define current density as: A current density J and an electric field E are established in a conductor when a potential difference is maintained across the conductor. The proportionality constant is called the conductivity of the conductor.

 Named after Georg Simon Ohm ( ) For many materials, the ratio of the current density to the electric field is a constant, (sigma), that is independent of the electric field producing the current. If the potential difference is constant, the current is constant. This is not a law of nature, but an empirical relationship found to be valid for certain materials (most metals)

For a segment of wire of length L: Resistance!

 The unit is the Ohm (Ω) The inverse of conductivity is resistivity!

For all metals, resistivity increases with temperature increase. some reference value usually at 20°C Temperature coefficient of resistivity

Divide both sides by time.

An emf is any device (generator/battery) that produces an electric field and thus may cause charges to move around in a circuit. Is an emf (ε) any different than a voltage source (V)? Any real emf has a certain amount of its own internal resistance, so the voltage that it will supply to a circuit between terminals is slightly different than its own potential difference. Both are measured in Volts.

An emf can be thought of as a charge pump. V is the terminal voltage Epsilon is the potential difference of the emf I is the circuit’s current r is the internal resistance of the emf R is the equivalent resistance of the circuit P is the power dissipated in circuit and emf device

I am Bunsen. Have you tried my burner? The sum of the currents entering any junction must equal the sum of the currents leaving that junction. The algebraic sum of the changes in potential across all of the elements around any closed loop must be zero. The sum of the currents entering any junction must equal the sum of the currents leaving that junction. The algebraic sum of the changes in potential across all of the elements around any closed loop must be zero.

Do you mean that Energy and Charge are conserved? Of course Bunsen, If charge is split between two branches it must flow down one path. it will not build up in a location or disappear. Also, a charge must gain as much energy as it loses throughout the circuit because it begins and ends at the same point. By the way, nice burner! Of course Bunsen, If charge is split between two branches it must flow down one path. it will not build up in a location or disappear. Also, a charge must gain as much energy as it loses throughout the circuit because it begins and ends at the same point. By the way, nice burner!

What is different about a circuit with a resistor and a capacitor than one with just a resistor? The current does not flow at a constant rate! Why is this? +-+- The charge stops flowing when a capacitor matches the battery voltage. It drains charge through the resistor after batter is disconnected.

C CRR No currentI ΔV R =0ΔV R =-IR ΔV C =Q 0 /C ΔV C =Q/C At time t=0 the switch is closed and the full capacitor discharges. From the loop rule…

Q and I are instantaneous values: