Consider the following circuit that contains a battery and six identical resistors:
The diagram has branch A with one resistor, connected to branch B with two resistors connected in parallel, and then branch B is connected to branch C with three resistors connected in parallel. The end of branch C is connected to a battery, and the end of branch A is connected to the opposite end of the battery.
Which resistor branch has the largest potential drop across it?
A
B
C
all the same
I'm thinking C just because each resistor has its own voltage drop and there are more resistors on branch C...is this right?
The same amount of current goes through each branch
say i through branch A and therefore R
now in branch b we get i/2 through each, half the voltage drop at A
and in branch c we get i/3 through each so
1/3 the voltage drop at A
The more the paths for the current, the less the voltage drop
Your thinking is partially correct. In a parallel circuit, the potential drops across each resistor connected in parallel are the same. However, the potential drop across each branch may not be the same.
In this circuit, the potential drop across each resistor will be the same since they are identical resistors. But the potential drop across each branch will depend on the total resistance in that branch.
Since all the resistors are identical, the total resistance in branch B (two resistors in parallel) will be half the resistance of a single resistor. Similarly, the total resistance in branch C (three resistors in parallel) will be one-third the resistance of a single resistor.
Now, considering the battery as the source of electromotive force (emf), the potential drop across each branch will be proportional to the total resistance in that branch. As the total resistance in branch C is the smallest, the potential drop across branch C will be the largest.
Therefore, the correct answer is: Branch C has the largest potential drop across it.
You're in the right direction! To determine which resistor branch has the largest potential drop across it, we need to consider the concept of series and parallel connections in circuits.
In this circuit, branch A has only one resistor, branch B has two resistors connected in parallel, and branch C has three resistors connected in parallel.
When resistors are connected in parallel, the potential difference (voltage) across each resistor is the same. So, the potential drop across branch B and branch C will be the same because both have resistors connected in parallel.
In contrast, branch A only has one resistor. Therefore, the potential drop across branch A will be different from the other branches since it has a single resistance.
Considering this information, we can conclude that branch A will have the largest potential drop across it.
Hence, the correct answer is A.