Electricity - DC Circuits and Resistors

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CURRENT

Current = flow of charge

Electric Current = rate at which charge moves across given cross sectional area

I = change in Q/ change in t measured in AMPERES

Q= net charge moving (across area in time)

Direct current - always flows in SAME DIRECTION

Current is assumed to be in the direction of the electric field (same as motion of + charge) - E & I in same direction

Metal Conductors

e- move, positive ions are fixed

Applied Electric field- e- have average drift velocity thus net current

No applied electric field - electron motion random, NO NET CURRENT

Current and Density of Charge Carriers

I = q x n x A x v

q= electron charge

n = density - (mass density of copper/mass of 1 copper atom)

A = area ( πr^2)

v = drift rate

Remarks:

-e- are pushed by electric field

-power companies sell energy not e-

AC- direction of flow reverses regularly

RESISTANCE

Electrical resistance

- opposition to flow of electrical current done through resistor

R=V/I measured in OHMS

R = p x (I/A)

p = resistivity

Energy sources in circuits

-Source of energy is required to maintain current

-this is EMF; electromotive force

-simple circuit = EMF and resistor (the work done/charge by energy source; measured in volts)

- in body this is Na+/K+ pump

-W=mgh

-gravity; does the work. W supplied by pump = U lost by water

Electrical System

-applied energy moves the charge

- charge moves in OPPOSITE DIRECTION to E

- thus electric field does negative work on charge

-energy field is conserved. so potential at end is same as the beginning

For the charge; energy transfer summary

1) energy acquired in battery = energy lost in resistor

2) stored chemical energy = heat (light) in resistor

Battery = source of stored energy (NOT CHARGE)

DC Circuits

- sum of potential changes around a closed path is 0 ( all change in v's = 0)

- E - IR = 0 where E= electromotive force

Power

-P= IV in WATTS

V= voltage drop

P=power absorbed by circuit element

Battery

- if - than battery is supplying power

- if + than battery is charging

Total power absorbed = total power supplied

kWh unit for energy 1000 x 3600 = 3.6x10^6 already in hours

Resistors in Series and Parallel

1) sum of potential charges = 0 (V's)

2)Current entering at any point must EQUAL the current leaving It = I1 + I2 i.e charge conservation

Series

R1 + R2 +R3 = Rt

Parallel

1/R1 + 1/R2 = 1/Rp

I = E/R where E = electromotive force

Capacitors in circuit

-in Biogical cells produce electric pulses

-called RC circuit (R and C in circuit)

Charging

-expontential increase

-T = RC

Discharging

-exponential decrease

-time scale of decay - T = RC

-drops by 63% every time

-Voltage = Vo = qo/C q = instananous charge on capacitor C = capacitance

-Current = joe ^ -t/T = qo/RC

Both

i = ioe ^-t/T

E - iR - q/C = 0 (intially q=0)

io = E/R