- #1

vcsharp2003

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- Homework Statement
- An electric circuit is as shown in diagram below. Determine the current through the 6 V battery.

- Relevant Equations
- Kirchhoff's Junction rule and Kirchhoff's Loop rule

I came up with the following set of equations. I try to express all currents in terms of ##I_1## and then substitute in the first equation to get the value of ##I_1##. Since ##I_4## needs to be determined and I have already expressed it in terms of ##I_1##, so it can be calculated. The problem is that I get a value of ##I_4= \dfrac {62}{25}## A when it's given in the book as 2 A. I am not sure if my approach of expressing all currents in terms of ##I_1## and then substitute in any equation is the correct way of solving such system of linear equations in 5 variables. We're not allowed to use online equation solvers, but we need to solve them manually.

Another problem is that how can I know that all equations I get by applying Kirchhoff's laws are independent, If I look at the first 3 equations I got then I can clearly see that when second and third equations are combined they give the first equation. I used to think that each application of Kirchhoff's rules to a different loop or junction will yield an independent equation, but clearly its not the case with the above set of equations.

**UPDATE 1**

I checked my solution using an online system of equations solver and the value of ##I_4= \dfrac {62}{25}## is correct. This can be seen at Solution from online equations solver. So, this means my initial approach of finding all current in terms of ##I_1## and then substitute in an equation to get the value of ##I_1## was correct.

**UPDATE 2**

I checked the solution in the book and it seems to be wrong when applying loop rules to loop 2 and loop 3. So, the answer of ##I_4= \dfrac {62}{25}## obtained from online equations solver seems to be correct, provided my initial set of equations obtained by applying Kirchhoff's laws were correct.

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