Parallel circuit multiple choice question

[DrKitten_Paws]

This past Monday I took an exam and got a 99, woot woot! But I can't seem to understand why I got the following question wrong:

Complete the following statement: A simple series circuit contains a resistance R and an ideal battery. If a second resistor is connected in parallel with R,
A) the voltage across R will decrease.
B) the current through R will decrease.
C) the total current through the battery will increase.
D) the rate of energy dissipation in R will increase.
E) the equivalent resistance of the circuit will increase.

I picked B since I used the following reseasoning: I_total = I₁ + I₂, therefore the current in R is decreased. My professor said that C is the correct answer. Although she tried to explain it, I couldn't understand it. Do you mind explaining it to me, please?

Thank you so much!

 

[Danger]

This is not in my area at all, and I probably would have scored only "1" on that test (if "A" is the correct answer.) My knowledge of electrical stuff is almost non-existent. Other than adding a few outlets to my house and rebuilding a bunch of things like VCR's, my experience is nil. The only reason that I think of "A" is that I once had to run a 6VDC motor from a 12VDC power supply. A friend who knows about this kind of stuff told me to parallel wire a resistor with the same rating as the load of the motor to cut the voltage in half. He called it a "voltage divider". While I can't say for sure why, it worked.

 

[berkeman]

This past Monday I took an exam and got a 99, woot woot! But I can't seem to understand why I got the following question wrong:

Complete the following statement: A simple series circuit contains a resistance R and an ideal battery. If a second resistor is connected in parallel with R,
A) the voltage across R will decrease.
B) the current through R will decrease.
C) the total current through the battery will increase.
D) the rate of energy dissipation in R will increase.
E) the equivalent resistance of the circuit will increase.

I picked B since I used the following reseasoning: I_total = I₁ + I₂, therefore the current in R is decreased. My professor said that C is the correct answer. Although she tried to explain it, I couldn't understand it. Do you mind explaining it to me, please?

Thank you so much!

Welcome to the PF.

Your professor is correct. As long as the battery is an ideal battery (no internal source resistance), the output voltage is indepent of output current. So the voltage across the parallel combination of R//R is the same as it was across the initial single R. And since I=V/R, that means that the current through the first resistor will not change when the second R is put in parallel with it. All that happens is that twice as much current is drawn from the battery when you put the 2nd R in parallel with the first.

Make sense now?

 

[CWatters]

I picked B since I used the following reseasoning: Itotal = I1 + I2, therefore the current in R is decreased.

I can see where you went wrong...

Your answer would be correct if an ideal battery was an current source. However an ideal battery is a voltage source.

For a constant voltage source the current Itotal isn't constant it depends on the load...

Itotal = Vbat/R1 + Vbat/R2

 

[Nickie]

Congratulations on your great exam score! It's always great to see students succeeding in their studies.

Regarding the multiple choice question, it's important to understand the concept of parallel circuits. In a parallel circuit, the current is split into multiple branches, with each branch having its own resistance. This means that the total current through the circuit is equal to the sum of the currents through each branch.

In the given scenario, adding a second resistor in parallel with R creates a new branch for the current to flow through. This means that the total current through the circuit will increase, as stated in option C. This can be mathematically represented as Itotal = I1 + I2, where I1 is the current through R and I2 is the current through the second resistor.

Your reasoning for selecting option B is partially correct, as the current through R will indeed decrease. However, this decrease in current is offset by the increase in current through the second resistor, resulting in an overall increase in the total current through the circuit.

Additionally, it's important to note that the voltage across R will remain the same, as the battery provides a constant voltage in a series circuit. This means that option A is incorrect.

I hope this explanation helps you understand the concept of parallel circuits and why option C is the correct answer. Keep up the good work in your studies!