Solving the Physics Riddle: A Current Across a Single Resistor

In summary: Today in physics lecture, our physics teacher left us with a riddle. The riddle involved an infinite grid of resistors with 1 ohm of resistance set up between every node of the grid. The question posed was, if a battery supplying a current of one amp is connected across a single resistor in the grid, what would be the current across that single resistor? Some students suggested the answer was one amp, but others speculated that it could be different depending on factors such as the voltage of the battery. The teacher's reasoning was not entirely clear, but it was suggested that the effective resistance of the infinite grid could be calculated using a factor of pi.
  • #1
Tom McCurdy
1,020
1
Today in physics lecture our physics teacher left us with a riddle.

If you had an infinite grid of resistors say with 1 ohm of resistance set up between every node of the grid and then you connected a battery that supplies a current of one amp through across a single resistor, what would be the current across that single resistor.
 
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  • #2
Is this like that question game on "Whose Line Is It Anyway?"
 
  • #3
Swiper no swiping!
 
  • #4
by the way the answer is 2/pi i believe
 
  • #5
Tom McCurdy said:
Today in physics lecture our physics teacher left us with a riddle.

If you had an infinite grid of resistors say with 1 ohm of resistance set up between every node of the grid and then you connected a battery that supplies a current of one amp through across a single resistor, what would be the current across that single resistor.
You do that by calling the effective resistance R and each resistor r.
Then (R+2r) and r in parallel equal R. (Draw a picture to see that.)
This gives 1/R=1/r+1/(R+2r), and I get R=(sqrt{3}-1) ohm.
Your phrase "a current of one amp through across a single resistor, what would be the current across that single resistor" is too confusing to determine what you mean by the current.
 
  • #6
Achuz, I don't think your reasoning is correct.

Tom McCurdy said:
... a battery that supplies a current of one amp through across a single resistor, what would be the current across that single resistor[?]

Clearly, the answer to the teacher's question (as posed, a riddle) is "one amp" (notice the battery is specifically configured to supply one amp across "that" resistor -- wording implies in situ!).

A more interesting question is to interpret that the battery instead provides one volt (ie. one amp across the one ohm in isolation), that is, asking how to calculate the effective resistance of the infinite grid - in which case a factor of pi in the result wouldn't sound unreasonable.
 
  • #7
cesiumfrog said:
Achuz, I don't think your reasoning is correct.



Clearly, the answer to the teacher's question (as posed, a riddle) is "one amp" (notice the battery is specifically configured to supply one amp across "that" resistor -- wording implies in situ!).

A more interesting question is to interpret that the battery instead provides one volt (ie. one amp across the one ohm in isolation), that is, asking how to calculate the effective resistance of the infinite grid - in which case a factor of pi in the result wouldn't sound unreasonable.

I thought it was one amp as well... but its not... I am going to try and find out if he meant the resistance across one set of nodes which Is 2/pi
 

1. What is the formula for calculating current across a single resistor?

The formula for calculating current across a single resistor is I = V/R, where I is the current in amps, V is the voltage in volts, and R is the resistance in ohms. This formula is known as Ohm's law.

2. How can I determine the resistance of a single resistor?

The resistance of a single resistor can be determined by using a multimeter, which measures the flow of current through the resistor. The resistance can also be calculated by dividing the voltage by the current, using the formula R = V/I.

3. What factors affect the current across a single resistor?

The current across a single resistor is affected by the voltage applied to the resistor, the resistance of the resistor itself, and the type of material the resistor is made of. Temperature can also play a role in the resistance of a resistor.

4. How does the length and thickness of a resistor affect the current?

The length and thickness of a resistor can affect the current by changing the amount of resistance in the circuit. A longer and thinner resistor will have a higher resistance, resulting in a lower current, whereas a shorter and thicker resistor will have a lower resistance and a higher current.

5. Can the current across a single resistor ever be higher than the applied voltage?

No, the current across a single resistor cannot be higher than the applied voltage. According to Ohm's law, the current is directly proportional to the voltage and inversely proportional to the resistance. Therefore, the current can never exceed the voltage in a single resistor circuit.

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