How to Determine the Resistance R1 in a Mixed Circuit Analysis?

[Logan Batson]

Homework Statement

The following circuit is given, and all voltage, current, resistance and power must be found for each resistor.

I have found the following information:

V_src = ?
I_src = .5A
R_src = ?
P_src = ?

V₁ = ?
I₁ = .5A
R₁ = ?
P₁ = ?

V₂ = 2.5V
I₂ = .25A
R₂ = 10
P₂ = .625W

V₃ = 2.5V
I₃ = .25A
R₃ = 10
P₃ = .625W

V₄ = 5V
I₄ = .25A
R₄ = 20
P₄ = 1.125W

How would I solve for the information of R₁?

Homework Equations

V = IR

The Attempt at a Solution

I originally had thought that V₁ is 5V, as the current is the same as the simplified parallel section. If the voltage from the cells is constant, and half of the circuit uses 5V, then I had assumed the other section would use 5V as well, as both currents are the same.

 

[phinds]

Homework Statement

The following circuit is given, and all voltage, current, resistance and power must be found for each resistor.

View attachment 235274

I have found the following information:

That makes it obvious that you have not provided a complete problem statement. WHERE have you "found" this information?

 

[Logan Batson]

That makes it obvious that you have not provided a complete problem statement. WHERE have you "found" this information?

The information given with the circuit is:

I₁ = 0.5A
V₃ = 2.5V
V₄ = 5V
P₃ = 0.625W

Sorry about not including this. Using Ohm's law, Kirchhoff's laws, and the equation P = VI, I had determined all other variables of the circuit using this information.

 

[phinds]

OK, so the circuit simplifies to R1 in series with a 10 ohm resistor that has 1/2 amp flowing through it and 5 volts across it. I don't see how this is enough information to tell anything about R1 and the voltage source --- they have a relationship, but you can't get numerical values. Are you sure this is all the info you were given?

EDIT: Oh, wait ... is it a requirement to get numerical values or is an algebraic expression OK?

 

[Logan Batson]

OK, so the circuit simplifies to R1 in series with a 10 ohm resistor that has 1/2 amp flowing through it and 5 volts across it. I don't see how this is enough information to tell anything about R1 and the voltage source --- they have a relationship, but you can't get numerical values. Are you sure this is all the info you were given?

EDIT: Oh, wait ... is it a requirement to get numerical values or is an algebraic expression OK?

An equation would work too! Thanks for helping

 

[phinds]

An equation would work too! Thanks for helping

OK. Can you get the equation? It should be really simple since you've got a simplified circuit that is two resistors and a power supply

 

[Logan Batson]

OK. Can you get the equation? It should be really simple since you've got a simplified circuit that is two resistors and a power supply

It should just be (Vt - 5) = 0.5(Rt - 10) right?

 

[phinds]

It should just be (Vt - 5) = 0.5(Rt - 10) right?

No, I think you are counting the equivalent resistor twice.

I get V - 5 = .5R1

 

[Logan Batson]

No, I think you are counting the equivalent resistor twice.

I get V - 5 = .5R1

Oh okay, I understand now. Thanks so much for your help