Solving Resistor Circuits: Find Currents in R & 10Ω Resistors

[Angie K.]

Homework Statement

The resistor R in the above figure has a resistance of 19.1 Ω.

a. Find the current in the resistor R.

b. Find the current in the 10-Ω resistor.

2. Homework Equations

Kirchhoff's Laws (Junction Rule and Loop Rule)

V=IR

The Attempt at a Solution

I figured out part a (I got 0.2844 A) and got it right.
I am not sure how to go about finding the current of the 10 Ohm resistor.
I know current flows through the path of least resistance.

I tried finding the voltage of the resistor R (because I have the current and the Resistance) and that's 5.43204 V and then using that same voltage (because for resistors in parallel, the voltage is the same) to figure out the current of the 10 Ohm resistor. (5.43204V/10Ohms=.543204 A) Which is the wrong answer.

Someone please clarify where I need to go from the information that I already have.

 

[jh001]

Be careful when you say "voltage of the resistor R". You actually mean the voltage drop (ie. voltage difference between the ends) is 5.43204. That means the other end (where the 10Ω is connected) is at 6 - 5.43204 = 0.56796V. You'll also need to find the voltage at the other end of the 10Ω to calculate the voltage drop, and only then can you calculate the current.

 

[Angie K.]

I meant the voltage drop. Sorry about that.

So that just gives me 5.43204 as the voltage drop of the other end and dividing by 10Ohms = .543204 Amps.
The one end has the voltage drop of .56796V and dividing that by 10Ohms , I get .056796 So now what do I do?

 

[SammyS]

Angie K.-- use the KVL to find Voltage drop across the 2Ω resistor & then find the current through same. etc.