As more branches are added to a parallel circuit, the overall resistance of the circuit does which of the following?. A) remains the same.B) definitely decreases.C) definitely increases.D) may increase.E) may decrease.
since
1/R = 1/r1 + 1/r2 + ...
the more parallel resistances you add, the larger the sum on the right grows.
Since 1/R is that sum, as 1/R grows, R shrinks.
me as well
As more branches are added to a parallel circuit, the overall resistance of the circuit may decrease (option E) or remain the same (option A).
In a parallel circuit, each branch provides an additional pathway for current to flow. As a result, adding more branches can potentially reduce the overall resistance of the circuit. This is because the total resistance in a parallel circuit is inversely proportional to the sum of the reciprocal of the resistances of each branch.
If the added branches have lower resistances than the existing branches, the overall resistance of the circuit will decrease. However, if the added branches have resistances equal to or higher than the existing branches, the overall resistance may remain the same.
To determine the effect of adding more branches to a parallel circuit on the overall resistance of the circuit, we need to understand the behavior of parallel circuits.
In a parallel circuit, each branch has its own path for the flow of current. As a result, the total resistance of the circuit decreases as more branches are added. This means that the answer to the question is option B) definitely decreases.
To explain further, let's consider a simplified scenario with just two branches in a parallel circuit. Each branch has its own resistance. When more branches are added, the total current flowing through the circuit can split and flow through multiple paths. This allows more current to flow overall, reducing the effective resistance of the circuit.
Mathematically, we can calculate the total resistance of a parallel circuit using the following formula:
1/RTotal = 1/R1 + 1/R2 + 1/R3 + ...
Where RTotal is the total resistance of the parallel circuit and R1, R2, R3, etc. are the resistances of the individual branches.
As you can see, adding more branches (R2, R3, and so on) decreases the reciprocal value of the total resistance (1/RTotal). Therefore, the overall resistance of the circuit definitely decreases as more branches are added.
Keep in mind that this explanation assumes that the resistance of each branch is not changing. If the resistance of any individual branch is modified, then the overall resistance of the circuit will be affected accordingly.