In a parallel circuit with 4 branches, each having a 100 ohm resistor, what is the total resistance?

In a parallel circuit, the total resistance can be calculated using the formula for parallel resistors, which is given by:

1/R_total = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

In this scenario, there are four branches, each with a 100 ohm resistor. Therefore, the equation becomes:

1/R_total = 1/100 + 1/100 + 1/100 + 1/100

This simplifies to:

1/R_total = 4/100

1/R_total = 0.04

To find the total resistance (R_total), you take the reciprocal:

R_total = 1 / 0.04 = 25 ohms

Thus, the total resistance in this parallel circuit is correctly identified as 25 ohms. This reflects the principle that in a parallel circuit, the total resistance is always less than the smallest individual resistance in the branches. The more branches you add with equal resistance, the lower the total resistance becomes.