7. Circuits and Magnetism

Current (I)

Movement of charge through a conductor over time (A = C/s)

The direction of current is…

Opposite to the flow of electrons

Current (I)

Movement of charge through a conductor over time (A = C/s)

The direction of current is…

Opposite to the flow of electrons

DC Circuit

Circuit in which current only flows in ONE direction

AC Circuit

Circuit in which current flow alternates

Electromotive Force

NOT actually a force; drives current (other word for voltage differentials)

Purpose of resistors in circuit:

Allows KE to transform into other energy sources (light or heat)

Ohm’s Law

V = IR

Power =

IV = I²R = V²/R

R =

V/I (Ohm’s Law)

Units of Resistance

Ohm (V/A)

Voltage Drop

Not evenly distributed through circuit, must use V = IR in multiple spots

Voltage Drop in Conductive Wire

0 V (in most cases) because in conductive wire, resistance is small and given V = IR, V should be negligible

Kirchoff’s Laws

1. Current in = Current out at a junction

2. V_source = ΣV_circuit (all voltage drops = source voltage)

Series

Components after a circuit added one after the other; uninterrupted current

Parallel

Components added in parallel; Splitting of current

R_s =

R₁ + R₂ + R₃…

In R_series, I_total =

I₁ = I₂….

In R_series, V_total =

V₁ + V₂….

Source Voltage and Voltage drops…

Cancel each other out because resistors work to lower voltage drop

For resistors in parallel, I_total =

I₁ + I₂ + …

For resistors in parallel, V_total =

V₁ = V₂ =…

1/R_p =

1/R₁ + 1/R₂ +…

Current flows easier in series or parallel resistors?

Parallel because resistors add reciprocally, so resistance will be lower, corresponding to better conductance

Ammeters

Device connected in series used to measure current (A) base; ideally has 0 resistance

Voltmeter

Device connected in parallel to measure voltage based on V=IR; should have the least current possible, and high resistance

Ohmmeters

Devices used to measure resistance based on current and voltage; two designs

Designs of Ohmmeters:

1. Known voltage supplied across resistor, current is measured

2. Known current is supplied across resistor, voltage drop measure

From measured and known values, resistance is calculated

Capacitor

Two separate, parallel conductive plates that accumulate charge; separated by non-conductive insulator (dielectric)

Dielectric Material

Non-conductive, insulating material used for capacitors

Capacitance

Degree to which a capacitor can store charge

Capacitance (C) =

Q/V (derived from Q = CV)

Two ways to increase charge in capacitor:

1. Increase capacitance

2. Increase voltage (drives accumulation of charge, emf)

Capacitor in a vacuum:

ε₀(A/d)

Function of insulating material in capacitor:

Prevents charges from equalizing (want charges to accumulate on plates)

For uniform electric fields ONLY:

E = V/d

PE for capacitors =

½CV²

Capacitors and Cell Physiology

Electric field generated across plasma membrane is similar to that generated between capacitor plates

Requirements for an object to be affected by magnetism:

1. The particle must be charged

2. The particle must be moving

Magnetic Fields

Act on charges, but ONLY moving charges (unlike E fields)

What generates magnetic fields?

Magnetic materials and moving charges

Diamagnetic

Materials that don’t generate magnetic fields and cannot become magnetized (Ex. Materials with paired electrons)

Paramagnetic

Materials that have unpaired electrons, random spins and are weakly attracted to magnetic fields that polarize the material

B =

(μ₀I)/2πr (T)

Right Hand Rule 1

1. Pointer points to I or v

2. Fingers curl to B

3. Thumb is the direction of F_B (reverse is charge is negative)

Right Hand Rule 2

1. Thumb is direction of I

2. Points curl to B

r =

mv/qB

F_{B, wire} =

IlBsinθ