Calculating Resistance, Current, Voltage Drop, and Power Dissipation: Analysis of a Series Circuit

The total resistance is simply the sum of the individual resistances, as given by this equation:

The current is found using Ohm’s law, $V=\text{IR}$. Entering the value of the applied voltage and the total resistance yields the current for the circuit:

The voltage—or $\text{IR}$ drop—in a resistor is given by Ohm’s law. Entering the current and the value of the first resistance yields

Similarly,

and

The three $\text{IR}$ drops add to $\text{12}\text{.}0\text{V}$, as predicted:

The easiest way to calculate power in watts (W) dissipated by a resistor in a DC circuit is to use Joule’s law, $P=\text{IV}$, where $P$ is electric power. In this case, each resistor has the same full current flowing through it. By substituting Ohm’s law $V=\text{IR}$ into Joule’s law, we get the power dissipated by the first resistor as

Similarly,

and

Power can also be calculated using either $P=\text{IV}$ or $P=\frac{V^2}{R}$, where $V$ is the voltage drop across the resistor (not the full voltage of the source). The same values will be obtained.

The easiest way to calculate power output of the source is to use $P=\text{IV}$, where $V$ is the source voltage. This gives

Note, coincidentally, that the total power dissipated by the resistors is also 7.20 W, the same as the power put out by the source. That is,

Power is energy per unit time (watts), and so conservation of energy requires the power output of the source to be equal to the total power dissipated by the resistors.