Parallelresistor

Parallelresistor refers to a configuration in electrical circuits where two or more resistors are connected to the same pair of nodes, so each resistor shares the same voltage across it. In this arrangement the current divides among the branches according to each branch’s resistance, while the voltage across every branch is identical.

The equivalent resistance of resistors in parallel is given by the reciprocal relation 1/R_eq = sum_i (1/R_i). For two resistors, R_eq = (R1*R2)/(R1+R2). More generally, R_eq decreases as more parallel paths are added, and it approaches the smallest individual resistance as one branch becomes much smaller than the others.

Current distribution follows I_i = V / R_i, where V is the common voltage across the parallel network. The total current is I_total = sum_i I_i. An equivalent expression is I_i = I_total * (R_eq / R_i). The power dissipated in each branch is P_i = V^2 / R_i, and the total power is P_total = V^2 / R_eq = sum_i P_i.

Practical considerations include tolerances and temperature coefficients of the resistors, which affect the exact parallel value. If a branch opens (infinite resistance), the others behave as if the open branch were not present. If a branch shorts (zero resistance), the total resistance collapses toward zero and the network draws large current. When assembling parallel resistors, it is important to ensure each component’s power rating is sufficient and to consider thermal effects that can alter resistance values.

Common uses of parallel resistor networks include achieving lower effective resistance values, providing redundancy, and enabling current-sharing configurations in certain circuit designs.