AP Physics B Summer Course 年 AP 物理 B 暑假班 M Sittig Ch 21: Circuits

Circuits  Circuits convert use electrical energy to do wondrous things: produce other kinds of energy, do calculations, store/send information, etc.  They are made possible when charges are put into motion by electric fields.

Current  Charge in motion is current (like an ocean current is ocean water in motion).  For historical reasons, current is defined as the movement of + charge, but we know that actually – charges move. Still, answers come out the same so no change…  I = ΔQ/Δt  Unit of current is C/sec, or Ampere (A).

Resistance  Remember conductors and insulators?  Good conductors have low resistance to current flow, and insulators vice versa.  R = ρL/A  ρ is resistivity, L is length of wire (m), A is cross-sectional area (m 2 ) of wire.  Unit of R is Ohms (Ω).

Resistivity

Ohm’s Law  For a given battery (voltage) hooked up to a resistor, the current is given by Ohm’s Law:  V = IR  Ohm’s law is cool, applies to whole circuits, as well as individual circuit components (parts of a circuit).

Example Problem

Practice Problem

Circuit Components

Series and Parallel  Series: components connected in a chain. Current can only take one path.  Parallel: components connected in a ladder. Current can split at junctions.  Mixed: both kinds of connections.

Resistors in series and parallel

Practice Problem  Find the equivalent resistance of this circuit:

Important Rules  Rule #1: When two resistors are in series, the amount of current that flows through each resistor is the same (only one path, no choice).  Rule #2: When two resistors are connected in parallel, the voltage across each resistor is the same (connected to same points on left & right).

Practice Problem  Which resistors have the same current?  Which resistors have the same potential difference?

V-I-R Chart  When you know two values, you can find the third value.  Use the Important Rules to fill in more values.

Example Problem

Practice Problem  A battery of voltage 20 V is connected in the circuit below, producing a current of 2 A in the 7 Ω resistor. Calculate: a) potential difference across the 7 Ω resistor b) potential difference across the two resistors in parallel c) current in the 12 Ω resistor d) resistance of the resistor R

Kirchoff’s Laws  Two conservation laws: conservation of charge, conservation of energy.  1. At any junction, the total current entering equals the total current leaving.  2. The sum of voltages around a closed loop is zero.

Kirchoff’s Laws  Label the currents (with direction).  Draw the loops (with direction).  Write the Kirchoff’s Laws equations.  Solve the system of equations.

Example Problem  Find I 1, I 2 and I 3.

Practice Problem

Circuits in the Lab  A bulb’s brightness depends on the power dissipated in the bulb.  Ammeters are connected in series and have a low resistance.  Voltmeters are connected in parallel and have a high resistance.

Capacitors in series and parallel  When capacitors occur in series, they add like resistors in parallel:  1/C eq = 1/C 1 + 1/C 2 + 1/C 3 + …  When capacitors occur in parallel, they add like resistors in series:  C eq = C 1 + C 2 + C 3 + …  The energy stored in a capacitor:  E = ½ CV 2

Practice Problem  If each capacitor has a capacitance of 4 nF, find the equivalent capacitance of each circuit.

RC Circuits  Just like in the movie, when an uncharged capacitor is connected to a battery it acts just like a wire.  After a while when the capacitor is charged, it cannot hold any more charge and acts like a large resistor.

Practice Problems  PPA6_ConcepTests_Ch_19.ppt PPA6_ConcepTests_Ch_19.ppt