Expression for voltage across resistor in circuit

[leroyjenkens]

Homework Statement

Write an expression for the voltage across R3 in terms of V0, R1, R2, and R3. Under what condition is the voltage across R3 approximately independent of the value of R3?

Homework Equations

I uploaded a picture.
I think Req = R1 + R2...
and 1/Req = 1/R1 + 1/R2...
Are what I need.

The Attempt at a Solution

Best thing I could think of doing was adding R2 and R3, and then add R1 to get this:

1/R2+R3 + R1, but I don't know how to include the voltage.

And I have no idea what it means by what condition is the voltage across R3 approximately independent of the value of R3.

 

[rbrayana123]

Homework Statement

Write an expression for the voltage across R3 in terms of V0, R1, R2, and R3. Under what condition is the voltage across R3 approximately independent of the value of R3?

Homework Equations

I uploaded a picture.
I think Req = R1 + R2...
and 1/Req = 1/R1 + 1/R2...
Are what I need.

There seems to be a confusion, common among many people, in your calculation of R_eq: Identifying which resistors are in series and which are in parallel. What helped me was watching these two videos: http://www.youtube.com/watch?v=0vqmQuo03Ss&list=PL4F8106B5158CB89E&index=13

In fact, the entire playlist was helpful on the whole subject of circuit analysis!

The Attempt at a Solution

Best thing I could think of doing was adding R2 and R3, and then add R1 to get this:

1/R2+R3 + R1, but I don't know how to include the voltage.

While finding R_eq first and finding the voltage drop across R₃ from there is a valid method (and I suggest you work it out for learning purposes), also consider the application of Kirchoff's Voltage Law

And I have no idea what it means by what condition is the voltage across R3 approximately independent of the value of R3.

Hmmm... I'm not exactly sure what this means either. However, I would suggest to consider how the behavior of voltages and currents differ in purely series and purely parallel circuits.

 

[rude man]

Homework Statement

Write an expression for the voltage across R3 in terms of V0, R1, R2, and R3. Under what condition is the voltage across R3 approximately independent of the value of R3?

Homework Equations

And I have no idea what it means by what condition is the voltage across R3 approximately independent of the value of R3.

What would happen if R1 << R3 or R2 << R3?

 

[NascentOxygen]

And I have no idea what it means by what condition is the voltage across R3 approximately independent of the value of R3.

Without R3, you can see R1 and R2 form a potential divider, dividing that potential V₀. R3 could represent a load that you wish to connect, to be powered by that smaller potential set by R1 and R2 and the voltage source.

As you know, the fact of connecting R3 will change the potential divider so the equation for the voltage across R2 must now involve a modification to include the value of R3.

If we denote the voltage across R2 as V_x, then your first task is to start with the basic potential divider equation:
V_x = R2/(R1+R2).V₀

and modify it to include R3, since R3 appears in parallel with R2. (At this stage, you have made no simplifying assumptions or approximations.)

Your second task then becomes more of a mathematical one ...

 

[Nickie]

I would like to thank you for providing a clear statement of the problem and the equations that you have attempted to use to solve it. The expression for the voltage across R3 can be written as V3 = V0 * (R3 / (R1 + R2 + R3)). This can be derived by using Kirchhoff's Voltage Law, which states that the sum of all voltages in a closed loop must equal zero. In this case, the voltage across R3 is equal to the voltage across R1 and R2 combined, which is then multiplied by the ratio of R3 to the total resistance (R1 + R2 + R3).

The condition for the voltage across R3 to be approximately independent of its value is when R3 is much larger than R1 and R2. This can be seen from the expression above, where as R3 approaches infinity, the voltage across R3 becomes equal to V0, regardless of the values of R1 and R2. This is because as R3 becomes larger, it becomes the dominant resistor in the circuit, and the voltage drop across it becomes the main factor in determining the voltage across R3.