Problem: I first began by denoting the very top middle node as A. At node A, I applied KCL: Σi = I - I_R - I_L => I = I_R + I_L So does this mean that I_R = I_L ? And the Answer is i?
How did you get from ? You need to define and in terms of using Ohm's law, . Just pretend the bottom terminal is ground (0V).
With the top node as A and bottom node a B, I = I_R + I_L simplifies to: I = (V_A - V_B) / (2R) + (V_A - V_B) / (R) = (V_A- V_B + 2V_A - 2V_B) / (2R) = 3V_A - 3V_B / (2R) Where would I go from here?
I also tried current division: I_R = [(2/3)R]/[2R] * I_total = V_AB / (2R) I_L = [(2/3)R]/[R] * I_total= V_AB / R So I_R > I_L Is this correct?
I_L > I_R It's a parallel circuit with three equal R's. Two of which are in one leg. I_L is .667 of I leaving I_R at .333 of I.
is 2x larger than . Another way to look at this is that current is inversely proportional to resistance, or . This gives: