Calculating Current in a Series Circuit

[warnexus]

Homework Statement

Homework Equations

I = E/(R sub_1 + R sub_2)

The Attempt at a Solution

So I tried using the same approach for part a and it did not produce the same result.

here's what i did:

I sub_2 = E sub_2/(R sub_2 + R sub_3)

E sub_2 was given as 1.7V

I sub_2 = (1.7V)/(5) = .34 A <- answer for part b

I also noticed E sub_3 was not given in the problem.

 

[aralbrec]

So I tried using the same approach for part a and it did not produce the same result.

You got lucky if you got the right answer using this approach for (a) :)

here's what i did:

I sub_2 = E sub_2/(R sub_2 + R sub_3)

If you rearrange that equation, this is what you are saying:

E₂ = I₂R₂ + I₂R₃

but this isn't true. The current through R₂ is I₂ but the current through R₃ is not I₂.

 

[warnexus]

for part a I used E sub_1 = I(R sub_1) + I(R sub_3)

really? i got lucky. when i got the answer, I thought I knew how it works but I guess I do not. =(

what should be going in my mind when I approach this type of problem. I was thinking in order to find the current I sub_2 I know it is across from I sub_3 and picked that one because it is closest. that's why I sub_2 was multiplied by R sub_3

 

[aralbrec]

what should be going in my mind when I approach this type of problem. I was thinking in order to find the current I sub_2 I know it is across from I sub_3 and picked that one because it is closest. that's why I sub_2 was multiplied by R sub_3

The current through a resistor results in a voltage drop and the total net voltage drop around a loop must be zero -- this is KVL.

In the equation you wrote:
E₂ = I₂R₂ + I₂R₃

the voltage drop across R₃ depends on the current through R₃, not the current through R₂.

So the correct equation would be:

E₂ = I₂R₂ + I₃R₃

NOTE: BE CAREFUL THAT THE SIGNS ON THESE CURRENTS AGREE WITH YOUR ASSUMED CURRENT DIRECTIONS

Similarly in (a) you wrote an equation for the left loop but you used the same current through R₁ and R₃, which is probably not right.

The correct equation would use the currents through R₁ (I₁) and R₂ (I₂) to find the voltage drops across R₁ and R₂.

After you've written those two equations, you'll notice you have three unknowns (I1, I2, I3) so one more equation is needed to solve the system.When I looked at the problem, I saw two loops (KVL) and would have used mesh analysis to solve it but the above is equivalent.

 

[warnexus]

thanks. i will use your input to finish this question.