Review

DC Circuits

Resistors in Series

Resistors in Parallel

Capacitors in Series and in Parallel

EMF and Terminal Voltage

Kirchhof’s Rules

Junction Rule

At any junction point, the sum of all currents entering the junction must equal the sum of all currents leaving the junction.

Loop Rule

The sum of the changes in potential around any closed path of a circuit must be zero.

Important: the number of equations must be the same as number of unknowns!!!

Take the signs:

For A Resistor:

- IR if your chosen loop direction is the same as the chosen current direction.

+ IR if the directions of loop and current chosen are opposite.

For A Battery:

+ if your loop direction moves from the negative terminal to positive.

- if your loop direction moves from the positive terminal to negative.

Circuits Containing a Resistor and a Capacitor

Magnets and Magnetic Fields

Important: do not confuse the magnetic poles and electric charges!

Important difference: the isolation of a single magnetic pole seems impossible! So far there is no confirmation of existence of magnetic monopole.

Electric current produces a magnetic field!!!

Direction of Magnetic Field Produced by a Current-Carrying

Wire: Right-Hand Rule

Magnetic Field Due to a Straight Wire

AmT

r

IB

/104

27

0

0

Force on Electric Current in a Magnetic Field

F=IlB sin

Important: the direction of the force is always perpendicular to the direction of the current and also perpendicular to the direction of the magnetic field.

Force between Two Parallel Wires

Parallel current in the same directions attract each other, antiparallel currents repel.

Faraday’s Law of Induction

If the flux through N loops of wire changes by the amount of B during time t, the average induced emf during this time is:

tN B

Lenz’s Law

An induced emf always creates a current whose magnetic field opposes the original change in flux.

Speed of EM Waves

00

1

v

Law of Reflection

The angle of incidence equals the angle of reflection.

Index of Refraction

The ratio of the speed of light in vacuum to the speed of light v in a given material is called the index of refraction, n of the material:

n=c/v

Snell’s Law

2211 sinsin nn

1

2sinn

nc

Important: total internal reflection can occur only when light strikes a boundary where the medium beyond has a lower index of refraction.

Real and Virtual Images

Finding the Image Position for a Curved Mirror

-ray 1 is drawn parallel to the axis; therefore it must pass along a line through F;

-ray 2 is drawn through F, as result is must reflect into parallel to the principal axis ray;

-ray 3 is chosen to be perpendicular to the mirror, and so is drawn so that it passes through C, the center of curvature; it will be reflected back on itself.

Mirror Equation

fdd io

111

The lateral magnification, m, of a mirror is defined as the height of the image divided by the height of the object:

o

i

o

i

d

d

h

hm

The Sign Convention

-the image height hi is positive if the image is upright, and negative if inverted, relative to the object;

-di and do are both positive if image and object are on the reflecting side of mirror, but if either image or object are behind the mirror, the corresponding distance is negative.

Finding the Image Position Formed by a Thin Lens

-ray 1 is drawn parallel to the axis; therefore it is refracted by the lens so that is passes along a line through the focal point;

-ray 2 is drawn on a line passing the other focal point F’ and emerges from the parallel to the axis;

-ray 3 is directed toward the very center of the lens, this ray emerges from the lens at the same angle as it entered.

1. The focal length is positive for converging lens and negative for diverging.

2. The object distance is positive if it is on the opposite side of the lens from where the light is coming; otherwise it is negative.

3. The image distance is positive if it is on the opposite side of the lens from where light is coming.

4. The height of the image is positive if the image is upright and negative if the image is inverted relative to the object.

The Lens Equation

Converging Lens: fdd i

111

0

Diverging Lens:

fdd i

111

0