Why do some resistors have a value of zero in a circuit with a short circuit?

In summary, a short circuit occurs when there is a connection with a very low (zero) resistance between two points in a circuit. This causes a large current to flow through the circuit, overpowering any other resistance. In the homework problem, one of the resistors was short-circuited while the other was not connected, resulting in both of them having zero contribution to the total resistance. Identifying which resistor is short-circuited can be done by observing the switch position and the resulting current flow.
  • #1
gprd3
4
0
I am having trouble understanding short circuits and would appreciate some help with it.

From what I understand, a short circuit occurs when we have a connection with a very low (zero) resistance is made between two points in a circuit. With R=0, the only resistance in our circuit would be the internal resistance of the battery. This causes a large current to go through the circuit Any clarifications, corrections, or additional information is greatly appreciated.

I also had trouble solving a homework problem that uses this concept. The following is the problem:

Homework Statement


In the circuit below, all four resistors are identical (R1 = R2 = R3 = R4 = R) and the battery has a voltage of 5.17 V.

21-p-018.gif


(a) When the switch is placed in position 1, the measured current in the battery is 1.14 mA. What is the value of each resistor?

Homework Equations



[; I=V/R;]
For resistors in series:
[;R_t_o_t=R_1+R_2;]
For resistors in paraller:
[;R_t_o_t=(1/R_1+1/R_2)^-^1;]

The Attempt at a Solution



Finding the total resistance of the circuit using Ohm's Law is easy:
[;R_t_o_t=V/I=5.17 V/1.14e^3 A= 4.54e^3 ohm;]

I then use [;R_t_o_t=R_1+R_2+R_3+R_4;] to find an expression for the total resistance in terms of R. Using this second equation with the value found with the first equation allows me to find R.

It turns out that [;R_2;] and [;R_3;] are both equal to zero! This is what I don't understand; WHY are they zero? I believe it has something to do with short circuits but I don't really understand what.

I appreciate your help.
 
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  • #2
gprd3 said:
I am having trouble understanding short circuits and would appreciate some help with it.

From what I understand, a short circuit occurs when we have a connection with a very low (zero) resistance is made between two points in a circuit. With R=0, the only resistance in our circuit would be the internal resistance of the battery. This causes a large current to go through the circuit Any clarifications, corrections, or additional information is greatly appreciated.

If a resistor is short-circuited, it means connected parallel with a zero resistance: The net resistance becomes zero, the resistor is eliminated from the circuit.

gprd3 said:
I also had trouble solving a homework problem that uses this concept. The following is the problem:

Homework Statement


In the circuit below, all four resistors are identical (R1 = R2 = R3 = R4 = R) and the battery has a voltage of 5.17 V.

21-p-018.gif


(a) When the switch is placed in position 1, the measured current in the battery is 1.14 mA. What is the value of each resistor?

Homework Equations



[; I=V/R;]
For resistors in series:
Rtot=R1+R2
For resistors in paraller:
Rtot=(1/R1+1/R2)-1

The Attempt at a Solution



Finding the total resistance of the circuit using Ohm's Law is easy:

Rtot=V/I=5.17 V/1.14e^-3 A= 4.54e^3 ohm

I then use Rtot=R1+R2+R4 to find an expression for the total resistance in terms of R. Using this second equation with the value found with the first equation allows me to find R.

It turns out that R2 and R3 are both equal to zero! This is what I don't understand; WHY are they zero? I believe it has something to do with short circuits but I don't really understand what.

I appreciate your help.


Redraw the circuit with the switch at position 1. One resistor is short-circuited. Which one? One resistor is not connected into the circuit. Which one?
Why do you think that both R2 and R3 are zero? The resistors are all equal, then the other two would be zero, too. Is it possible?

ehild
 
  • #3
ehild said:
Redraw the circuit with the switch at position 1. One resistor is short-circuited. Which one? One resistor is not connected into the circuit. Which one?

Why do you think that both R2 and R3 are zero? The resistors are all equal, then the other two would be zero, too. Is it possible?

ehild

That makes sense. So resistor 3 is not part of the circuit so it is not taken into consideration when calculation the total resistance. Is that correct? But I do not know which one is short circuited, how can I tell?
 
  • #4
gprd3 said:
That makes sense. So resistor 3 is not part of the circuit so it is not taken into consideration when calculation the total resistance. Is that correct?

yes, it is correct.

gprd3 said:
But I do not know which one is short circuited, how can I tell?

The switch is at position 1. You have a single wire connected parallel to resistor R2: it is short-circuited. The wire has zero resistance. The current chooses the zero resistance path, and nothing flows through R2.
(Or you can say that the total resistance of R2 and the zero-resistance wire is zero.)

ehild
 

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  • #5
That makes so much sense. So it isn't that R2 and R3 are zero, what happens is that R2 is short circuited and R3 is not connected to the circuit and therefore, they do not contribute any resistance to the total resistance of the circuit! Thank you!
 
  • #6
you are welcome.

ehild
 

1. What is a short circuit?

A short circuit is an electrical circuit in which the current flows along an unintended path. This can occur when two conductive materials with different voltages come into contact or when there is a break in the insulation of a wire.

2. How does a short circuit occur?

A short circuit can occur due to a number of reasons, such as damaged wires, faulty appliances, or incorrect wiring. It can also be caused by overloading a circuit with too many devices or by using devices with different voltage requirements.

3. What are the potential dangers of a short circuit?

Short circuits can be dangerous as they can cause sparks, fires, and electric shocks. They can also damage appliances and electrical systems, leading to costly repairs.

4. How can short circuits be prevented?

Short circuits can be prevented by regularly inspecting and maintaining electrical systems and appliances. It is important to use devices with the correct voltage and to avoid overloading circuits. Using surge protectors can also help prevent short circuits.

5. How are short circuits diagnosed and fixed?

To diagnose a short circuit, a technician will use a multimeter to check for continuity in the circuit and locate the area where the current is flowing along the unintended path. Short circuits can be fixed by repairing or replacing damaged wires, fuses, or circuit breakers. It is important to only attempt to fix a short circuit if you have the necessary knowledge and skills, as it can be dangerous to work with electricity.

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