Sensing

Definitions

Current is defined as the rate of flow of charge.

Potential difference is energy transferred per unit charge.

Potential difference is the difference in energy per unit change from one point in a circuit to another. p.d. is measured in Volts () using a voltmeter. Conceptually, p.d. is the energy per unit charge transferred from electrical energy to other forms of energy, whilst e.m.f (electromotive force) is the energy per unit charge transferred into electrical energy from other forms of energy.

Resistance

Resistance is opposition to the flow of charge. It is measured in Ohms ().
Ohm's Law states that:

Power is defined as energy over time:

Drift Velocity

In a conductor carrying a current, the electrons will experience a force from negative to positive. This causes an average displacement over time, which causes drift velocity.

Where:

is the charge carrier density (number of charge carriers per unit volume), in
is the cross-sectional area of the wire, in
is the drift velocity, in
is the charge on each charge carrier, in .

Conductance

Conductance is the amount of current that flows through a component for each volt of p.d. applied across it. It is the reciprocal of resistance, and is measured in Siemens ().

Resistance and conductance rules

For components in parallel, the voltage across each component is the same:

Giving the general rule that conductances in parallel sum. As conductance is the reciprocal of resistance, this gives the rule.

For components in series, the current through each component is the same:

Considering equal currents gives:

By Ohm's law, this means the sum of reciprocals of conductances is equal to resistance. Thus, the conductance, which is the reciprocal of resistance, must be given by:

Conductances in series act like resistances in parallel. As conductance is the reciprocal of resistance, this gives the rule that resistances add in series.

Resistivity and conductivity

Resistivity () is a property of a material that described the extent to which the material opposes the flow of electric current. The resistance of a piece of material depends on its resistivity, size and shape. The resistance of a wire with cross-sectional area and length made from a material with resistivity (in ) is given by:

Conductivity () is a measure of a material's ability to conduct electricity. The unit of conductivity is (as conductivity is the reciprocal of resistivity). The conductance of a wire is given by:

Internal Resistance

An ideal cell has no internal resistance, but a non-ideal cell can be modelled as an ideal cell and a resistor. The terminal difference of a cell is given by:

Where:

is the terminal potential difference, in
is the electromotive force, in
is the current, in
is the internal resistance of the cell, in .

Kirchhoff's Laws

Kirchhoff's current law (1st Law) states that the current flowing into a node must be equal to the current flowing out of it. This is a result of conservation of charge.
Kirchhoff's voltage law (2nd Law) states that in any complete loop in a circuit, the directed sum of all voltages across components is zero, or alternatively the sum of e.m.f.s is equal to the sum of p.d.s. This is a result of conservation of charge and energy.

Potential Dividers

In a potential divider, the ratio of voltages across each series component is equal to the ratio of resistances: