Question

Which of the following statements would be true for a simple circuit with a 9V battery connected to two 3 ohm resitors connected in parallel?

Answer 1

What are the statements?

Answer 2

None, apparently

Answer 3

A. The effective resistance would be the sum of the resistors, 6Ohms total.
B. Adding additional resistors in parallel will increase the amount of current flowing through the circuit.
C. Voltage drop across each of the individual resistors is 9V.
D. Current in both branches of the circuit is the same.
E. An electron traveling once around the circuit would travel through both of the resistors.

Answer 4

@Bobo-i-bo and @sparker

Answer 5

Well you can eliminate some choices right away

A) how do you add parallel resistors? Not R1 + R2 so this one is out

B) resistors resist current...so adding more will only decrease the current

D) in parallel, voltage is the same across both parallel beaches while the current splits...so this is gone too

What else can you eliminate?

Answer 6

E.

Answer 7

So you can safely choose E.

Answer 8

"B) resistors resist current...so adding more will only decrease the current" Adding resistors in parallel opens new ways for the current to flow. Adding resistors in parallel actually decreases the total resistance of the circuit, and thus increases the intensity of the current in the circuit. Unless I missed something ?

Answer 9

Nope you are absolutely correct @Eleuthere !

Answer 10

A and E are both INCORRECT statements and B, C, and D are all CORECT statements.

A is an incorrect statement because since the resistors are in parallel, the sum of the resistors would be\[\frac{ 1 }{ R _{total} }=\frac{ 1 }{ R _{1} }+\frac{ 1 }{ R _{2} }\] and when you plug in 3Ω for both resistances (R1 and R2) you get 1.5Ω as your total resistance (Rtotal). If the resistors were in series then the sum of the resistances would be 6Ω, but this is not the case.

B is a correct statement because the current of the circuit before another resistor is added in parallel calculated with the equation\[V=IR\]where V is the total voltage (9V)
I is the current
and R is the total resistance (which we calculated as 1.5Ω)
So when you solve for the current, you get 6 Amperes for the current before the resistor is added.
When adding another resistor in parallel would make the total resistance 1Ω and plugging it back into the V=IR equation, you get 9 Amperes for the new circuit, therefore, the current is increased.

C is a correct statement because the resistors are in parallel and the voltage drop is always the same in each path of the parallel circuit.

D is a correct statement only if "the branches" of the circuit is referring to the two pieces of wire that each contain a resistor that are parallel with each other. If this is not what the branches are referring to, then please let me know and I can explain whatever it is referring to. Assuming I am correct, again using the equation\[V=IR\]and you calculate the current that passes through each resistor, using 9Volts for V and 3Ω for R, you get 3Amperes as your current for both since both the resistance and voltage drop are the same.

E is definitely an incorrect statement because if the electron only travels around the circuit once, then when it goes to the parallel resistors, it has to choose a path, one or the other; it cannot travel through both in one trip.

I hope this helps!(: