Parallel circuits

Formula for equivalent resistance

When several resistors are connected in parallel, their combined effect on the circuit can also be expressed as a single equivalent resistance. In this case, the equivalent resistance is found by summing the reciprocals of each connected resistance, using the following formula:

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ +…+ 1/R_n

The voltage applied to each branch is the same, whilst the total circuit current is shared among the different branches according to their respective resistance values. In this way, the equivalent resistance represents the total opposition to the flow of current in a circuit with multiple available paths.

Practical example

Suppose we have three resistors connected in parallel with values of 10 Ω, 20 Ω, and 30 Ω. The equivalent resistance of the circuit is found by adding the reciprocals of each resistance:

1/R_eq = 1/10 + 1/20 + 1/30 = 0,100 + 0,050 + 0,033 = 0,183

R_eq = 1/0,183 = 5,46 Ω

This means that, from the perspective of the power supply, the set of resistors behaves as a single resistance of approximately 5.46 Ω. The voltage applied to each branch is the same, whilst the total current supplied by the source is divided among the three resistors according to their values. For example, if the source provides 12 V, the currents will be 1.2 A through the 10 Ω resistor, 0.6 A through the 20 Ω resistor, and 0.4 A through the 30 Ω resistor, which adds up to a total of 2.2 A.