1 Electrical Quantities and Ohm’s Law

Charge and current

Electric circuits involve the movement of electric charge and the transfer of energy. The quantities used to describe circuits indicate how much charge moves, how strongly it is driven, how much a material opposes its motion, and how quickly energy is transferred.

Electric charge is a property of matter, measured in coulombs ($\text{C}$) and often represented by $Q$ or $q$. The magnitude of the charge of one electron is approximately $1.602 \times 10^{-19}\,\text{C}$.

Electric current is the rate at which charge passes a point:

Here, $I$ is current in amperes ($\text{A}$), $Q$ is charge in coulombs, and $t$ is time in seconds. Since $1\,\text{A} = 1\,\text{C/s}$, a current of $2\,\text{A}$ carries $2\,\text{C}$ of charge past a point each second. Rearranging the current equation gives $Q = It$.

Voltage and potential difference

Voltage, or potential difference, describes the energy transferred per unit of charge between two points:

Voltage is measured in volts ($\text{V}$), where $1\,\text{V} = 1\,\text{J/C}$. A $9\,\text{V}$ source can transfer $9\,\text{J}$ of energy for each coulomb of charge that passes through it. Voltage is always measured between two points.

Resistance and Ohm’s law

Resistance describes how strongly a component opposes current. It is measured in ohms ($\Omega$), with $1\,\Omega = 1\,\text{V/A}$.

For many resistors under steady conditions, voltage, current, and resistance are related by Ohm’s law:

The relationship can be rearranged to find current or resistance:

For a fixed resistance, increasing voltage increases current. For a fixed voltage, increasing resistance decreases current. Ohm’s law describes ohmic components, for which voltage is proportional to current under the conditions considered; not every component has this proportional relationship.

For example, a $6\,\Omega$ resistor connected across a $12\,\text{V}$ source carries a current of:

Power and energy

Electrical power is the rate of energy transfer. It is measured in watts ($\text{W}$), where $1\,\text{W} = 1\,\text{J/s}$. For a circuit element:

For an ohmic resistor, substituting Ohm’s law gives two further forms:

Energy transferred over a time interval is power multiplied by time:

Energy is measured in joules ($\text{J}$). Household electricity use is often stated in kilowatt-hours ($\text{kWh}$), with $1\,\text{kWh} = 3.6 \times 10^6\,\text{J}$.

For the $6\,\Omega$ resistor connected to a $12\,\text{V}$ source, the current is $2\,\text{A}$, so its power is:

If it operates for $5$ minutes, or $300\,\text{s}$, the energy transferred is:

The charge passing through it during that time is:

Checking the energy using voltage and charge gives $VQ = (12\,\text{V})(600\,\text{C}) = 7200\,\text{J}$, consistent with the calculation using power and time.