Resistors in Parallel

Resistors in parallel are multiple resistors connected across the same two nodes or points in an electrical circuit.  In a parallel configuration, the resistors share the same voltage across their terminals while having different paths for the flow of electric current.  In other words, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.

The advantage of connecting resistors in parallel is that the total resistance decreases compared to the resistance of any individual resistor.  This allows for a larger current to flow through the circuit since the overall resistance is reduced.  It is similar to providing additional pathways for the flow of current, which lowers the overall resistance.  Additionally, the voltage across each resistor in parallel is the same since they are connected across the same nodes.  This property can be useful in applications where different resistors need to operate at the same voltage level.

Another important consideration when connecting resistors in parallel is the power dissipation.  Each resistor will dissipate power based on its individual resistance, and the total power dissipated in the parallel combination can be calculated.  It's worth noting that when resistors are connected in parallel, care must be taken to ensure that the power ratings of the resistors are suitable for the total power dissipation and that the individual resistors are capable of handling the current flowing through them.  Resistors in parallel find application in various circuits, such as voltage dividers, current limiting circuits, and load sharing configurations

 

Resistors in Parallel formula
\((1\;/\;R_t) \;=\;  (1\;/\;R_1)  +  (1\;/\;R_2)  +  (1\;/\;R_3) \; + ...  +\; (1\;/\;R_n) \)
Symbol	English	Metric
\(R_t\) = total resistance	\(\Omega\)	\(kg-m^2\;/\;s^3-A^2\)
\(R_1, R_2, R_3, R_n\) = resistance	\(\Omega\)	\(kg-m^2\;/\;s^3-A^2\)