Схемотехніка резисторів: Закон Ома, серійні та паралельні кола

Series Resistance

When resistors are connected in series, the total resistance (R_total) is the sum of their individual resistances (R1, R2, ... Rn): R_total = R1 + R2 + ... + Rn. This linearity allows us to use algebraic equations to solve for unknown resistor values.

In a series circuit, the current flowing through all components is identical. The voltage divides proportionally according to each component's resistance. For example, if you have two resistors in series, the total voltage (V) will be divided into two parts such that V = V1 + V2, where V1 is across R1 and V2 is across R2.

The key characteristic of a series circuit is its predictable behavior. Changes to one resistor directly affect the current and voltage distribution throughout the entire network. This makes it relatively easy to analyze and design circuits using Ohm's Law.

V = I * R           (Ohm's law)
P = I * V = I^2 * R = V^2 / R      (power dissipated as heat)

Parallel: same voltage, currents add

Resistors in parallel have multiple paths for the current to flow, so the same voltage V is across every one of them. The total current drawn from the source is the sum of the individual currents (Kirchhoff's current law: the sum of currents entering a junction equals the sum of currents leaving it), so the equivalent resistance is given by the formula: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. Adding a resistor in parallel always decreases total resistance and increases current for a fixed supply voltage.

Series: same current, voltages add

Resistors in series share a single endpoint, so each one experiences the same current flowing through it. The total voltage across the series combination is the sum of the individual voltage drops across each resistor (Kirchhoff's Voltage Law: voltage into a node equals voltage out). The equivalent resistance follows the addition rule R_total = R1 + R2 + ... + Rn. Adding a resistor in series always increases total resistance, because it provides an additional path for current to flow.

series:    R_total = R1 + R2 + ... + Rn
parallel:  1/R_total = 1/R1 + 1/R2 + ... + 1/Rn
special case, two resistors in parallel:  R_total = (R1*R2) / (R1+R2)

Series Resistance

The total resistance (R) of a series circuit is the sum of all individual resistances (r). Therefore, R = r1 + r2 + r3 + ...

In a series circuit, the current (I) is constant throughout. The voltage drop across each resistor is proportional to its resistance.

The power (P) dissipated in a series circuit is calculated as P = I^2 * R, where I is the total current and R is the total resistance.

Calculating Power Dissipation

Every resistor converts electrical energy to heat at a rate P = I²R = V²/R. This is fundamental to understanding how much heat will be generated in a circuit.

Circuit designers pick series resistors to limit current (protecting an LED, for instance) and parallel combinations to lower an effective resistance or split current between multiple load paths. A low-resistance parallel path can silently carry most of the current, and most of the power, if the parallel resistances are mismatched.

Frequently asked questions

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