Circuit with Resistors and a Battery

In summary, in this circuit with five resistors and a battery, the unknown resistor RX has a current of zero and therefore all the current that flows through R2 also flows through RX. The potential at the ends of R4 is the same because the current through it is zero. In order to find the magnitude of the voltage across R2, we can use the equation V=IR and the known current through R1. To find the value of RX, we need to consider the voltage divider formed by R2 and RX in series. The voltage across R1, V1, is not necessarily 12 as initially thought, but depends on the values of R1 and R3.
  • #1
hawaldko
12
0

Homework Statement


A circuit is constructed with five resistors and a battery as shown. The battery voltage is V = 12 V. The values for the resistors are: R1 = 54 Ω, R2 = 142 Ω, R3 = 148 Ω, and R4 = 109 Ω. The value for RX is unknown, but it is known that I4, the current that flows through resistor R4, is zero.

http://imgur.com/IwvnK

http://imgur.com/IwvnK

There is a picture of the circuit.

I know the current through R1 is 0.0594059406.

Here are my questions:

1) What is V2, the magnitude of the voltage across the resistor R2?
2)What is I2, the magnitude of the current that flows through the resistor R2?
3)What is RX, the value of the unknown resistor RX?
4)What is V1, the magnitude of the voltage across the resistor R1?


Homework Equations



I=V/R

The Attempt at a Solution



1) Essentially, I thought the voltage across V2 should be 12, the same as the battery because the voltage should be equal across parallel circuits. This answer is wrong, and I don't really understand why. I don't know how to use I=VR without knowing the current, which I know won't be the same and not knowing Rx.

2) I think I need the answer from 1 to do this one, and I can just use V=IR, but I don't know how to do it was Rx instead of a real number

3) Absolutely no idea.

4) I think this should be 12, but I don't think it is because of the first problem.

I am really having difficulty with this problem and would appreciate any help.
 
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  • #2
If the current through R4 is zero, then all the current that flows through R1 also flows through R3. Similarly, all the current that flows through R2 must flow through Rx.

If the current through R4 is zero, what does that say about the potential at each end of R4?
 
  • #3
So the potential has to be the same? How can it be the same if there are different resistors before it? I'm sorry, I'm just really not getting it.
 
  • #4
hawaldko said:
So the potential has to be the same? How can it be the same if there are different resistors before it? I'm sorry, I'm just really not getting it.

The current is zero so there cannot be a difference in potential. So you need to look at how the potential at either end of that resistor is established. Consider R1 and R3. Two resistors in series form a voltage divider. How does the voltage divide across the two resistors?
 
  • #5
So does that mean the the voltage across each of them is 6?
 
  • #6
hawaldko said:
So does that mean the the voltage across each of them is 6?

No. How does it depend upon the resistor values? Can you work it out?
 

What is a resistor?

A resistor is an electronic component that limits the flow of current in a circuit. It is typically made of a material that has a high resistance to the flow of electricity.

What is a battery?

A battery is a device that stores chemical energy and converts it into electrical energy. It is made up of one or more cells that contain a positive and negative electrode, as well as an electrolyte.

How does a circuit with resistors and a battery work?

In a circuit with resistors and a battery, the battery provides a source of electrical energy. The resistors limit the flow of current in the circuit, causing a voltage drop. This allows the circuit to control the amount of current flowing through it.

What are the different types of resistors?

There are several types of resistors, including fixed resistors, variable resistors, and special resistors such as thermistors and photoresistors. Fixed resistors have a set resistance value, while variable resistors allow for the adjustment of resistance. Special resistors have unique properties that make them useful in specific applications.

How do you calculate the total resistance in a circuit with multiple resistors?

To calculate the total resistance in a circuit with multiple resistors, you can use Ohm's Law, which states that resistance is equal to voltage divided by current. If the resistors are connected in series, you can simply add their individual resistances together. If they are connected in parallel, you can use the formula 1/R(total) = 1/R1 + 1/R2 + 1/R3 + ..., where R(total) is the total resistance and R1, R2, R3, etc. are the individual resistances.

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