1.7 - Charge and current
● ***Current: rate of flow of charge
Q(charge[C])
○ *** I (current [ A ])=
t (time [s ])
Drift velocity
● ***
−3
I (current [ A ])=n(charge carrier density [m ]) ×q (total charge of charge carriers [C ])× v (drift veloci
where q is usually the charge of 1 electron: 1 e = 1.6 × 10-19 C
○ nA: no. of charge carriers per metre length
○ nAv: no. of charge carriers passing by a point per second
○ → nqvA: charge passing a point in a second, C s−1 ≡ A
○ Derivation of equation:
■ ∆ V ( volume of wire)=A ( cross sectional area)× ∆ x (length of wire)
■
∆ N (total no . of charge carriers )=n(charge carrier density)× ∆ V =nA ∆ x
■
∆ Q( total quantity of charge)=nA ∆ x × q(charge on each charge carrier )
■ Suppose each charge carrier takes a time ∆t to travel the
distance ∆x,
∆Q ∆x
=nAq
∆t ∆t
∆Q ∆x
■ ∵ =I , =v , ∴ I =nqva /¿
∆t ∆t
Metals, semiconductors, insulators and resistance
● The higher the value of n, the more conductive the material is
○ Metals - typically n = 1028 ~ 1029 m-3
○ Insulators (eg glass, polystyrene) - virtually 0 charge carriers (at RTP)
○ Semiconductors (eg Ge [≈1019], Si [≈1017]) - able to conduct BUT not as well
as metals
■ “The ability of semiconductors to conduct is greatly enhanced by
increasing their temperature/adding ‘impurity atoms’”
1
● ***Current: rate of flow of charge
Q(charge[C])
○ *** I (current [ A ])=
t (time [s ])
Drift velocity
● ***
−3
I (current [ A ])=n(charge carrier density [m ]) ×q (total charge of charge carriers [C ])× v (drift veloci
where q is usually the charge of 1 electron: 1 e = 1.6 × 10-19 C
○ nA: no. of charge carriers per metre length
○ nAv: no. of charge carriers passing by a point per second
○ → nqvA: charge passing a point in a second, C s−1 ≡ A
○ Derivation of equation:
■ ∆ V ( volume of wire)=A ( cross sectional area)× ∆ x (length of wire)
■
∆ N (total no . of charge carriers )=n(charge carrier density)× ∆ V =nA ∆ x
■
∆ Q( total quantity of charge)=nA ∆ x × q(charge on each charge carrier )
■ Suppose each charge carrier takes a time ∆t to travel the
distance ∆x,
∆Q ∆x
=nAq
∆t ∆t
∆Q ∆x
■ ∵ =I , =v , ∴ I =nqva /¿
∆t ∆t
Metals, semiconductors, insulators and resistance
● The higher the value of n, the more conductive the material is
○ Metals - typically n = 1028 ~ 1029 m-3
○ Insulators (eg glass, polystyrene) - virtually 0 charge carriers (at RTP)
○ Semiconductors (eg Ge [≈1019], Si [≈1017]) - able to conduct BUT not as well
as metals
■ “The ability of semiconductors to conduct is greatly enhanced by
increasing their temperature/adding ‘impurity atoms’”
1
