CURRENT OF ELECTRICITY
Electric charge
charge(+/-), Q which flows past a pt. in time, t if current, I is constant is defined by Q = It (Q = coulomb, C, 1C = 1As)
if I not const, Q = I dt (area under I-t graph) [Q = It => I = dQ/dt => Q = I dt]
I = nAve [n = # of conduction electrons per unit volume, A = cross-sectional area of wire, v = drift speed/velocity of e^-s, e = electric charge] (I = nAvQ; Q for both + & - charges) (v depends on ion vibration; vib. ^: v decreases (more collisions)
dirⁿ of conventional current = dirⁿ of +ve charges (+ > -)
current, I = rate of flow of charge

Potential difference
-pd bet 2 pts = E converted from elec E to other forms of E when unit charge passes from 1 pt to another
pd = E converted/charge => V= E/Q (1 V = 1 J/C)
-potential at a pt in circuit: usually pd bet pt & arbitrary zero (arbitrary zero: electric earth)
V = E/Q = E/t ÷ Q/t = P/I => pd = power/current (1 V = 1 W/A)

Resistance
-electric property of material that makes moving charges -dissipate energy
-ratio of pd to current, R= pd/current = V/I (R: , ohm, 1 = 1 V/A)

Ohm's Law: I through a metallic conductor is directly ∝ to the pd across its ends, provided temp remains const

grad of V-I graph = R
grad of I-V graph = 1/R



1/R = conductance (S, siemens, 1 S = ^-1)

R ∝ l/A => R = k l/A = l/A ( = resistivity = RA/ l; m)
(m); conductor: ~10⁷, semiconductor: ~10², insulator: ~10¹⁰
R_t = R₀(1 + t) [ = temp coefficient of resistance]
= (R_t - R₀) / R₀t


I = nAve: as T
  -metals; n: ~ const (), v: => I: => R:
  -thermistor; n: , v: => I: => R:   -insulator; n: => I: => R:
  -semiconductor; n: , v: => I: ( in charge carriers more significant)=> R:

conductivity = 1/ resistivity = 1/
I = V/R = VA/(l) = conductivity x VA/ l I ∝ conductivity, pd, cross-sectional area & I ∝ 1/wire length

Electromotive force
-E converted from other forms to elec E per unit charge
emf, = energy converted (generated) / charge supplied, = E/Q (: volts, V, 1 V = 1 J/C)
emf of source = pd across source terminal as I 0

Internal Resistance

When I flows through resistor: voltmeter shows pd across battery & resistor (voltage drop due to voltage drop in int R)
E transferred per second within battery = E (transferred in circuit & in overcoming int R) per second
I = I²R + I²r
=> = IR +Ir
=> V = IR = - Ir = emf - voltage across int R = terminal pd (pd shown on voltmeter)
good voltmeter: v. high R- accurate reading: terminal pd very close to battery emf

V = IR = -Ir (r: const)
if R (resistance of resistor) is varied and I measured => V-I graph plotted to obtain r


Efficiency
efficiency = power (output / input) = power [to external circuit / used(supplied)] = I²R/I = IR/ = IR/(IR+Ir) = R/(R+r)


efficiency 1 unless r = 0
R >> r, efficiency 1
R = r, efficiency = 50% (max power)


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