- #1
RadiationX
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My professor gave us the task of proving the current division law for two resistors in parallel. I know that the voltage across parallel resistors is the same, and that the sum of the branch currents adds to the sum of the total current.
Here is the question:
Prove that [tex]I_1= \frac{I_sR_2}{R_1 + R_2}[/tex] ; [tex] I_s[/tex] = the source current.
Now, this is what I know: [tex] I_s= I_1 +I_2[/tex]
That is about as far as I can get. I know that I need to manipulate [tex] I_s= I_1 +I_2[/tex] somehow to derive [tex]I_1= \frac{I_sR_2}{R_1 + R_2}[/tex].
This is the first time I have ever been assigned a proof and I don't have any experience solving them, so my tool set is kind of lacking.
As a side note I would like to be able to prove 'simple' theorems like this. I think it would give me a level of insight that I don't currently have.
Here is the question:
Prove that [tex]I_1= \frac{I_sR_2}{R_1 + R_2}[/tex] ; [tex] I_s[/tex] = the source current.
Now, this is what I know: [tex] I_s= I_1 +I_2[/tex]
That is about as far as I can get. I know that I need to manipulate [tex] I_s= I_1 +I_2[/tex] somehow to derive [tex]I_1= \frac{I_sR_2}{R_1 + R_2}[/tex].
This is the first time I have ever been assigned a proof and I don't have any experience solving them, so my tool set is kind of lacking.
As a side note I would like to be able to prove 'simple' theorems like this. I think it would give me a level of insight that I don't currently have.
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