Voltage and Current Divider Equations for Simplified Circuit | Homework Solution

[roinujo1]

Homework Statement

Homework Equations

• V_x=V_t(R_x/(R_x+R_t))
• I_x=I_t(R_t/(R_t+R_x))

The Attempt at a Solution

• I first simplified the circuit to only one resistor to get the total I_t and got 0.0168 A.
• I next made the split the circuit where there was a current I_a going through the 150 and 40 ohm resistors and a I_b going into the 75,60, and 30 ohm resistors.
• I then used current division to get I_a and I_b.

Now here is where the trouble is? I think I can easily get v₂, but how do I get v₁? I don't understand what resistor I should use to calculate it.

Any help is much appreciated.

 

[gneill]

$v_1$ is across both the 150 and 75 Ohm resistors. That is, they share the same potential difference. So how are those resistors connected to each other?

You might also want to re-check your circuit simplification to find the total current. The value that you found doesn't look right to me. Share your work if you're unclear on any steps.

 

[jaus tail]

• I next made the split the circuit where there was a current I_a going through the 150 and 40 ohm resistors and a I_b going into the 75,60, and 30 ohm resistors.

Maybe look at this sentence. The current going through 150 ohm and 40 ohm isn't exactly same.

 

[roinujo1]

Thanks for the responses. So, based on what was said, I tried it through a different approach

• I simplified the circuit into one with 1 resistor with a R_total=135 ohms. I did this by saying that since the 150 and 75 ohm resistors have the same voltage, they are in parallel and combined them to make a 50 ohm resistor in series with the 40. This left me with two 90 ohm resistors in parallel that I combined and added the 90 ohm resistor near the voltage source. I found I_total= 22.2 mA
• Now, I used current division to get the current going through the 50 ohm(found from 150 and 75) and 40 ohm, which are now in series. Did the same with the 60 and 30 ohm resistors. However, when calculating the resistance for the rest of the circuit excluding R_x(lets say for the 60 and 30 in this case), would R_{rest of circuit}=(50+40)||(90)?

 

[jaus tail]

However, when calculating the resistance for the rest of the circuit excluding R_x(lets say for the 60 and 30 in this case), would R_{rest of circuit}=(50+40)||(90)?

I didn't understand this. Why do you need resistance for rest of circuit? Once you've found the currents in the branches using current divider rule, you can find voltage across them using ohm's law.

The 50 and 40 ohm would be in parallel with 90 ohm on left, if there were another voltage source on right and you were using superposition theorem or if you were finding Thevenin's resistance seen from right side to left. But that's not needed here.

On a side note you can also solve the problem without finding currents in branches. Maybe try that and see if your answers match.