DC Circuits Currents. Resistors. Batteries. Kirchhoff’s Loop Rules. Power

Examples of Circuits

Current: flow of charge Average current: I av = Charge  Q flowing across area A in time  t Instantaneous current: differential limit of I av Units of current: Coulomb/second=Ampere (A)

Direction of the current Direction of current is in direction of flow of positive charge or, opposite direction of flow of negative charge

Current density J (1) J : current/unit area points in the direction of the current Units A/m 2

Current density J (2) If the ara is not perpendicular to the current A n area or surface perpendicular to the direction of the current  : angle between normal to A and current

Why does current flow? If an electric field is set up in a conductor, charge will move (making a current in the direction of E) Note that when current is flowing, the conductor is not an equipotential surface (and E inside  0)!

Microscopic picture (1) Drift speed is velocity forced by applied electric field in the presence of collisions, it is typically 4x10 -5 m/s, or 0.04 mm/s! To go one meter at this speed takes about 10 hours Thermal velocity is around 10 3 km/s ! How can this be?

Microscopic picture (2) v d : drift velocity n : number of carriers per unit volume q : charge of each carrier (normally e) A : suface perpendicular to v d

Conductivity and resistiviy Ability of current to flow depends on density of charges & rate of scattering. Two quantities summarize this:  : conductivity  : resistivity

Microscopic Ohm’s Law  And  depend only on the microscopic properties of the material, not on its shape

The voltage drops in a resistor The electric field brings about a voltage drop in a resistor

What is the relationship between  V and current? Ohm’s Law (1)

R has units of ohms (  )=Volt/Amp Ohm’s Law (2) Then, units of  :  m and  :  -1 m -1

Examples of Circuits

Symbols for circuit elements

Electromotive force -Battery Moving from the negative to positive terminal of a battery increases your potential Think: Ski Lift

Internal resistance Real batteries have an internal resistance, r, which is small but non-zero Terminal voltage: Real battery=ideal battery in series with a resistance

Sign conventions - Resistor Moving across a resistor in the direction of current decreases your potential Think: Ski Slope Voltage drop: Voltage decreases in the direction of the current

Sign conventions - Capacitor Moving across a capacitor from the negatively to positively charged plate increases your potential

Resistors in series The same current I must flow through both resistors or

Resistors in parallel Voltage drop across the resistors must be the same or

Measuring V, I, R

Measuring Potential Difference A voltmeter must be hooked in parallel across the element you want to measure the potential difference across Voltmeters have a very large resistance, so that they don’t affect the circuit too much

Measuring Current An ammeter must be hooked in series with the element you want to measure the current through Ammeters have a very low resistance, so that they don’t affect the circuit too much

Measuring Resistance An ohmmeter must be hooked in parallel across the element you want to measure the resistance of Here we are measuring R 1 Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery)