Current Divider Circuit (Find a Resistance)

[johnsmith7565]

Homework Statement

Find The Value Of R That Will Carry a 4 A Of Current To Flow Through The 80 Ohm Resistor In The Circuit Shown.

Relevant Equations

Parallel Circuit rules and Series circuit rules, i0 = (R1)/(R1+R2)is, where “is” is the source current, R1 and R2 are the resistances, and i0 is the current across a resistor.

The resistors are all in series , with exception of R, so I added them together and then used the current divider equation to solve for R, and I got 720 ohms. The textbook says R should be 30 ohms. I’m completely lost.

 

[gneill]

Hi @johnsmith7565 ,

Welcome to Physics Forums.

Note that the $60 Ω$ resistor is not in series with the $40 Ω$ and $80 Ω$ resistors; The existence of the resistor $R$ precludes that.

What you can say is that 20 A enters the top node from the direction of the source, and that it must divide between the two parallel branches. Write your current division expression so that it divides the 20 A as required using only the three resistors of the parallel branches.

 

[johnsmith7565]

Hi @johnsmith7565 ,

Welcome to Physics Forums.

Note that the $60 \Ohm$ resistor is not in series with the $40 \Ohm$ and $80 \Ohm$ resistors; The existence of the resistor $R$ precludes that.

What you can say is that 20 A enters the top node from the direction of the source, and that it must divide between the two parallel branches. Write your current division expression so that it divides the 20 A as required using only the three resistors of the parallel branches.

I still don’t understand. So the 40 ohm resistor and the 80 ohm one are in series so I add them, and now my equation is 4=(20)(120/R+120) and R is still too large.

 

[gneill]

I still don’t understand. So the 40 ohm resistor and the 80 ohm one are in series so I add them, and now my equation is 4=(20)(120/R+120) and R is still too large.

I think you'll want to take a closer look at the current divider expression. Let's say you have two parallel resistances A and B with some total current $I$ being split between them. Then you can write:

$I_A = I \cdot \frac{B}{A + B}$

$I_B = I \cdot \frac{A}{A + B}$

Make sure that you get your numerator correct!