Electrical power in direct current (DC) circuits

Relationship between Voltage, Current, and Power

In a direct current circuit, electrical power is obtained by multiplying the applied voltage by the current flowing, according to the fundamental expression:

P = V · I

where

P is power in watts (W)

V is voltage in volts (V)

I is current in amperes (A)

This relationship indicates how much energy per second is being transferred to a component.

When the element is a resistor, Ohm’s law allows us to express the power in equivalent ways:

P = I² · R

P = V² / R

where

R is resistance in ohms (Ω)

The first expression shows how power increases with the square of the current, while the second relates power to the square of the voltage. These equations allow us to analyze how power varies depending on the circuit conditions and form the basis for understanding power distribution and losses in more complex configurations.

Power Distribution in Circuits

In a direct current circuit, power is not distributed arbitrarily: it directly depends on how voltage and current are divided according to the circuit configuration. In other words, each element absorbs a different portion of the total power based on its position and its resistance value. Analyzing this distribution helps us understand why some components dissipate more energy than others and how losses change when we modify the circuit topology. This analysis is essential for correctly sizing resistors, estimating heating, and assessing the overall efficiency of an electrical system.

Power Distribution in Series

In a series circuit, all elements are traversed by the same current, so the power absorbed by each resistor depends only on its resistance. Since the power expression for a resistor is P = I² · R, the resistor with the highest value always dissipates the most power because it multiplies the same current by a larger R. Moreover, the voltage drop across each resistor is proportional to its value, so the power distribution follows exactly the same proportion: more resistance means more voltage and, therefore, more power absorbed.

This behavior has a direct consequence: the total power consumed in the circuit is the sum of the individual powers, but the distribution is not uniform. If a resistor doubles its value, it also doubles the power it dissipates; if it halves its value, its power is halved. That’s why, in a series circuit, the higher-value resistors are the ones that heat up the most and require greater attention when sizing their nominal power. Analyzing this distribution is essential to avoid overheating and ensure that each component operates within its limits.

Power Distribution in Parallel

In a parallel circuit, all elements share the same voltage, so the power absorbed by each resistor depends on its value and the current flowing through its branch. Since each branch conducts a different current, power is calculated using the expression P = V² / R, which clearly shows that the lower-value resistors dissipate more power because they allow more current to flow. This behavior is the opposite of series circuits: here, the fixed voltage applied to each branch is what matters, not the common current.

The total power consumed in a parallel circuit is the sum of the power in each branch, but the distribution is not uniform either. If a resistor decreases its value, the current flowing through it increases, and consequently, the power it absorbs increases; if its value increases, its power decreases. That’s why, in a parallel circuit, the smaller resistors heat up the most and require greater attention when choosing their nominal power. Understanding this distribution is essential to anticipate the thermal behavior of the circuit and to properly size each branch according to the load it must support.

Power Received, Absorbed, and Losses in the Circuit

In a direct current circuit, power is not limited to what the loads consume, such as resistors, lamps, or motors. There is always some power lost in the circuit itself: in the conductors, in the internal resistances of the sources, and in any element that, without being a useful load, dissipates energy as heat. These losses are an inevitable part of the real operation of any electrical system.

The power delivered by the source is therefore split into two blocks: the useful power, which reaches the loads to perform the intended work, and the lost power, which is dissipated in undesired elements of the circuit. The larger these losses, the smaller the fraction of power that actually reaches the load. This difference between what the source delivers and what the load receives allows us to define the efficiency of the circuit.

Analyzing these losses is fundamental for understanding why an apparently simple circuit does not deliver all its energy to the load, why some components heat up more than expected, and how the total circuit resistance influences overall performance. Based on this analysis, design decisions can be made: reduce unnecessary resistances, shorten cables, choose suitable components, or properly size the power that the source must supply.