Find Current I1 in 7.5 Ω Resistor with Kirchhoff's Rule

[deenuh20]

Homework Statement

In the circuit below: (a) Find the current I1 that passes through the 7.5 Ω resistor.

Homework Equations

Kirchhoff's Rule--Loops

The Attempt at a Solution

This was a problem in my textbook. The answer is .65 A, but I don't understand how to get that. I tried Kirchhoff's rule by finding equivalent R between A & B and Then finding equivalent R between A & C then finding I, Then breaking I into I1 and I2 (according to the parallel resistances between A & B)

However, I still didn't get the answer, .65 A. Was my approach correct, or is there another way? Thank you.

 

[AlephZero]

Your plan of how to solve it is OK, and when I did it that way I got 0.65A.

If you can't find your mistake, show your working, then somebody can check through it.

 

[m2003]

Your approach using Kirchhoff's rule is a valid method for finding the current I1 in the 7.5 Ω resistor. It is possible that there may have been a calculation error in your steps, which resulted in a different answer. It is important to double check your calculations and make sure you are using the correct values for the resistors and voltage sources in the circuit. Another approach that can be used to find I1 is to use Ohm's law, which states that the current through a resistor is equal to the voltage across the resistor divided by its resistance. In this case, the voltage across the 7.5 Ω resistor is the same as the voltage across the 10 Ω resistor, which is 12 V. Therefore, using Ohm's law, we can calculate I1 as 12V/7.5Ω = 0.8 A. This is very close to the given answer of 0.65 A, which may be due to rounding errors. Overall, your approach using Kirchhoff's rule was correct, but it is always important to double check your calculations and use alternative methods to verify your results.