Chapter 9: Electric Current, Potential Difference and Resistance

Circuit symbols and diagrams

Electric components and their circuit symbols

Electric Current
It is the rate of flow of electric charge past a point.
current=charge/time
I=ΔQ/Δt
So, we can get equation for charge as: ΔQ = IΔt

Charged Particles
Current is the flow of charge particle called charge carriers. Electrons carry negative charge which is approximately equal to -1.6 × 10^-19C.
The magnitude of charge is elementary charge:
Elementary charge e = 1.6 × 10^-19C

Equation for current
Number density n:
It is the number of free electrons, per unit volume in a material.

A current I in a wire of cross sectional area A. The charge carriers are mobile conduction electrons with the drift velocity v.

Number of electrons = number density × volume of wire
= n × A × l
Charge of electrons = number × electron charge
= n × A × l × e
We can find current I as it is the charge that flows in time t, and current = charge/time
I=n×A ×l ×e⁄t
Substituting v for l/t
I=nAve
I=nAvq
Where v is drift velocity and q is the charge of each particles.
From these equations we can know that:
If the current increases, drift velocity must increase i.e. v α I
If the wire is thinner, the electrons move more quicker for given current v αI/A

Potential Difference
Potential difference V is defined as the energy transferred per unit charge. The potential difference between two points, A and B, is the energy per unit charge as charge moves from point A to point B.
Electromotive force e.m.f. is defined as the total work done per unit charge when charge flows round a circuit.

Electrical Resistance
It is defined as the ratio of potential difference to the current.
resistance=(potential difference)/current
R=V/I
Ohm
It is the unit of resistance. The ohm is equivalent to “1 volt per meter” that is:
1Ω = 1V A^-1
Electric Power
It is the rate at which energy is transferred. Power P is measured is Watt (W).
Power= (energy transfered)/(time taken)
P= W/(∆t )= V∆Q/∆t=V(∆Q/∆t)
The ratio of charge to time, ∆Q/∆t, is the current I. so,
P = VI
Power = Potential difference × current
P = I^2R
P = V^2/ R

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