DC circuits are electrical circuits where current flows in one direction. The three fundamental quantities are voltage, which is the electrical potential difference that drives current; current, which is the flow of electric charge through a conductor; and resistance, which opposes the flow of current. Think of voltage as electrical pressure, current as the flow rate of electrons, and resistance as the restriction in the path.
Ohm's Law establishes the mathematical relationship between voltage, current, and resistance. The basic form is V equals I times R. We can rearrange this equation to solve for current as I equals V over R, or for resistance as R equals V over I. This linear relationship means that if we double the voltage while keeping resistance constant, the current will also double. Let's see how changing these values affects our circuit.
Series circuits have components connected in a single path, creating only one route for current to flow. The key characteristic is that current remains constant throughout the entire circuit, while voltage divides across each component. The total resistance equals the sum of all individual resistances. In our example with a 12-volt source and resistors of 2, 4, and 6 ohms, the total resistance is 12 ohms, giving us a current of 1 ampere. Each resistor drops voltage proportional to its resistance value.
Parallel circuits provide multiple paths for current flow, with components connected across common junction points. Unlike series circuits, voltage remains constant across all parallel branches, equaling the source voltage. However, current divides among the branches based on each branch's resistance. The total resistance is calculated using the reciprocal formula, resulting in a value smaller than the smallest individual resistance. In our example with 12 volts and resistors of 6, 4, and 3 ohms, each branch carries different current amounts that sum to the total current of 9 amperes.
Mixed circuits combine both series and parallel elements, requiring systematic analysis to solve. We start by identifying parallel sections and calculating their equivalent resistance using the parallel formula. Then we treat this equivalent resistance as a single component in series with other elements. In our example, resistors R2 and R3 are in parallel, giving us 3 ohms equivalent resistance. This combines in series with R1 for a total of 9 ohms. Using Ohm's law, we find the total current, then work backwards to determine individual branch currents and voltage drops across each component.