How to Choose Resistors for Desired Currents in a Circuit

[Mosaness]

1.Choose a voltage v < 2.5 V and values for the resistors R1, R2, R3, and R4 in
the circuit of Fig. 3.90 so that i1 =1 A, i2 =1.2 A, i3 =8 A, and i4 = 3.1 A.

Homework Equations

KCL/KVL/OHms Law

The Attempt at a Solution

If I_s = I₁ + I₂ + I₃ + I₄,

Then, I_s = [itex]\frac{v}{R_eq}[/itex]

R_eq = [itex]\frac{1}{R₁}[/itex] + [itex]\frac{1}{R₂}[/itex] + [itex]\frac{1}{R₃}[/itex] + [itex]\frac{1}{R₄}[/itex].

After this, I get stuck...

 

[Bhumble]

You're over thinking the problem. For parallel branches, the voltage is the same to all branches of the node. For simplicity choose 1V and for R1 choose 1 ohm so that I1 = 1A. Now you have the voltage and current for each branch so just solve for resistance via ohm's law.

 

[Mosaness]

You're over thinking the problem. For parallel branches, the voltage is the same to all branches of the node. For simplicity choose 1V and for R1 choose 1 ohm so that I1 = 1A. Now you have the voltage and current for each branch so just solve for resistance via ohm's law.

So because we can choose any v that is less than 2.5V, you picked 1V correct?

 

[Mosaness]

Taking V as 1A and using the given values for the currents, I solved for R1, R2, R3, and R4:

R1 = 1V/1A = 1Ω

R2 = 1V/1.2A = 0.83Ω

R3 = 1V/8A = 0.125Ω

R4 = 1V/3.1A = 0.323Ω

Is this correct?

 

[Bhumble]

Looks good. And if for some reason you need the voltage to be higher than you can just scale the resistance proportionately to maintain the same current.