if three resistances in parallel circuit are all equal, the total resistance is ___ the resistance of any on branch.
three times the current for the same voltage
V = i R
V = 3i (R/3)
so one third
In a parallel circuit, when all resistances are equal, the total resistance is smaller than the resistance of any individual branch. To understand why this is the case, let's break it down step by step.
In a parallel circuit, each branch provides an additional pathway for the current to flow. This means that the total current is divided among the branches, creating multiple paths for the current to follow.
Now, consider resistors in parallel. Since all resistances are equal, each branch will have the same resistance. Let's call this resistance "R."
When the current reaches the junction where the branches are connected, it splits into multiple paths. According to Ohm's Law (V = IR), the current flowing through each branch is inversely proportional to its resistance. Since the resistance in each branch is the same (R), the current is divided equally among them.
Now, let's calculate the total resistance (RT) of the parallel circuit. The total resistance is calculated using the formula:
1/RT = 1/R1 + 1/R2 + 1/R3 + ...
Considering we have three resistances of equal value (R), the formula becomes:
1/RT = 1/R + 1/R + 1/R
Simplifying further, we get:
1/RT = 3/R
To find RT, we can take the reciprocal on both sides of the equation:
RT = R/3
Therefore, the total resistance (RT) is equal to one-third (1/3) of the resistance of any individual branch (R). Since RT is smaller than R, we can conclude that the total resistance is smaller than the resistance of any individual branch.