Physics Class 4 - Electrostatics, Capacitors, Batteries, Resistors

What is electric charge? Symbol, units.

Q or q

Units: [q] = C (coulombs)

Positive or negative

What is elementary charge?

e = 1.6 × 10^-19 C

Smallest possible unit of charge; exists in multiples of this

Ex: 1 electron, 1 proton

What is coulomb’s law?

F_E = k|Q||q|/r²

Q and q are each charges that interact

k = 9 × 10⁹ N*m²/c²

r is distance between charges

F_E can be attractive (opposites attract) or repulsive (like repels like)

Inverse square law

What is superposition of forces?

Allows determination of F_E when >2 charges in the system

Net effect is the vector sum of the force from each individual charge

Multiple instances of the same force

What are electric fields?

Vector created by source charges that permeate the space around them

F_E = qE

E is a vector

F_E is positive when in the same direction as E, negative when in the opposite direction

What is the electric field at a point a distance away from the source charge?

E = k|Q|/r²

E is positive going away from the source, negative towards (figure out superposition first)

Units = N/C = V/m

What are electric field lines?

Summary of all electric field vectors in space

Direction of electric field is tangent to the field line

Strength corresponds to density of field lines

Electric field is in the same direction as acceleration

This applies to the dipole of water molecules that connect

What is electric potential?

Scalar field created by source charges that permeate space around them

Equipotentials are closed curves instead of straight or curved arrows

Electric potential = kQ/r

Units: J/C = V (+, -, or 0)

Use for scalar problems (work, energy, speed)

What is electric potential energy? Work by electric potential energy?

change in PE = q (change in electric potential) = qV

W_{by E} = -change in PE_E

change in KE = - change in PE in absence of non-conservative forces

Spontaneous: change in PE < 0

What is change in PE_E for positive charges for spontaneous action?

change in PEE = q change in electric potential

(-) = (+)(-)

Positive charges want to accelerate to regions of lower electric potential

What is change in PE_E for negative charges for spontaneous action?

change in PEE = q change in electric potential

(-) = (-)(+)

Negative charges want to accelerate to regions of higher electric potential

What is a capacitor?

Circuit element used to store charge and energy

Two conducting surfaces separated by insulator (dielectric)

C = k(epsilon₀) A/d in F(farads)

k = dielectric number (1 for vacuum and air, >1 for other insulators)

Epsilon₀ constant (no need to know)

A = area of conducting surface

d = distance between two conducting surfaces

What is a batterie?

Source of voltage (potential difference) → not source of charge or current

Positive terminal (longer line): higher potential

Negative terminal (shorter line): lower potential

Voltage of batterie: V = change in voltage between + and - terminals

Symbol for potential is phi (circle w/vertical line)

What charge is stored by a capacitor when connected to batterie in closed circuit?

Q = CV

Q = charge

C = capacitance

V = voltage difference between plates of the capacitor

What is the electric field in a capacitor?

When charged, perpendicular to the plate, from positive to negative

Magnitude of the field is E = V/d

V = voltage of plates

d = separation of plates (a constant)

What is the point charge equation of electric field?

E = k|Q|/r²

What is the energy stored by a capacitor (potential energy)?

PE_cap = ½ QV = ½ CV² = Q²/2C

Area under a QV graph

What is a dielectric?

Insulating materials that polarize in an electric field

Induced dielectric field opposing the external electric field → E_net drops, and so does V

Battery has greater voltage than capacitor and can move charge into it

What is dielectric breakdown?

Insulator is ionized by too large of an external electric field, allowing charge to move through it

Results in a spark

What is capacitance of a capacitor when a dielectric is inserted into it?

If you disconnect battery, then insert dielectric? If you insert while still connected?

C = kC₀

k = dielectric number

What is a conductor?

Material in which charges move freely

No net movement of charge → current = 0

How do you get a current through conductors?

Impose a potential energy difference → induces a net movement of charge

delta PE_E = q delta phi

(-) = (-)(+)

What is the flow rate of a charge through a conductor (current in a conductor)?

I = Q/t

Charge per second

Units A = C/s

What is resistance?

Constant of proportionality between voltage and current it induces

How much an object opposes the flow of charges through it

V = IR

R is constant

Units: omega

What is resistivity (rho)?

How much a material opposes flow of charges through it

Units: omega * m

What are resistors?

Segments of a circuit with known resistance

Use up energy in a circuit as heat/light

Represent via jagged lines

With one resistor and one battery, how do you find total current?

Voltage of battery determines voltage across the resistor

Use Ohm’s law (V = IR)

What is a series?

One path through resistors

Same current through each

R_equivalent = sum of (R₁ + R₂ +… R_n)

What does it mean for resistors to be in parallel?

Multiple paths through resistors (not necessarily geometrically parallel)

Same voltage across each

1/R_eq = sum of (1/R₁ + 1/R₂ +…1/R_n)

How do you find R_eq for two resistors?

R_eq = (R₁*R₂)/(R₁ + R₂)