Parallel resistors and ammeter problem

In summary, the student mistakenly connected a perfect ammeter in parallel with one of the two identical resistors and got a reading of 0.40A. The correct reading would have been 0.20A if the ammeter was correctly connected in series with two resistors. This can be determined using Ohm's Law and Kirchhoff's first law, which states that the sum of the currents entering a junction must equal the sum leaving the junction.
  • #1
Gregg
459
0

Homework Statement



A student mistakenly connects a perfect ammeter (i.e one of negligible resistance), in parellel with one of the two of the two identical resistors. The ammeter reads of 0.40 A.
What would the reading have been if he had correctly connected the ammeter in series with two resistors? The cell also has negligible resistance.

http://upload.lhurgoyf.net/gal/Other/physics0908.JPG

Homework Equations



[itex] \Delta Q = I\Delta T[/itex]
Kirchhoff's first law

The Attempt at a Solution



At this stage in the book, only the two relevant equations/law have been discussed. The answer is 0.20A but I'm not exactly sure why and how I would get this answer. It seems that it can only possibly be relevant to Kirchhoff's, the sum of the currents entering a junction must equal the sum leaving the junction.

The current in between the two resistors (before the junction) must be 0.40A then, so it seems that the reading on the ammeter should be 0.40A. I don't think I understand the concept properly, a clue would be good.
 
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  • #2
Have you considered the current in the first resistor as shown in the diagram?
 
  • #3
You're making this too complicated; as you suspected, you're not seeing the concept. You need only Ohm's Law at this point.
 
  • #4
[itex]I=\frac{V}{R}[/itex]

[itex]\therefore I \propto \frac{1}{R}[/itex]

[itex] I_1 = \frac{V}{R} = 0.40[/itex]

[itex] I_2 = \frac{V}{2R} = \frac{I_1}{2} = 0.20[/itex]
 

Related to Parallel resistors and ammeter problem

What is the purpose of parallel resistors?

Parallel resistors are used to decrease the overall resistance in a circuit. This allows for a larger amount of current to flow through the circuit, improving its efficiency.

How do you calculate the equivalent resistance of parallel resistors?

The equivalent resistance of parallel resistors can be calculated using the formula 1/Req = 1/R1 + 1/R2 + 1/R3 ... where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances in the circuit.

What is the role of an ammeter in a circuit?

An ammeter is used to measure the amount of current flowing through a circuit. It is typically connected in series with the circuit, meaning the current flows through the ammeter.

How do you connect an ammeter to a circuit with parallel resistors?

An ammeter should be connected in series with one of the parallel resistors. This will allow it to measure the total current flowing through that resistor and the rest of the parallel resistors in the circuit.

What happens to the current in a parallel circuit when one resistor is removed?

If one resistor is removed in a parallel circuit, the total current in the circuit will increase. This is because the overall resistance decreases, allowing for a larger amount of current to flow through the circuit.

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