Question

Using Kirchhoff's rules, calculate the current in R1 with the directions indicated in the figure below. Assume that R1 = 1.00 kohm, R2 = 3.00 kohm, R3 = 5.00 kohm, E1 = 75.0 V, E2 = 60.0 V and E3= 90.0 V.

Calculate the current in R₂.

Calculate the current in R3

Find the magnitude of the potential difference between points c and f.

Answer 1

Here, the easy way to do this is node analysis because there is only one node at c or b because they are the same voltage. Call that voltage V. Let f be ground.
(V-75)/1k + (V-60)/3k + (V-90)/5k = 0
Multiply the equation by 1k
V(1 +1/3 + 1/5) = 75 + 60/3 + 90/5
V = (75 + 20 + 18)/(1 + 1/3 + 1/5) = 113/1.53 = 73.86 V = Vcf <-----------
i1 = (73.86-75)/1k = -1.14 mA <--------------
i2 = (73.86 - 60)/3k = 4.62 mA <--------------
i3 = (73.86-90)/5k = -3.23 mA <-------------
Here the negative sign shown that the directions of i1 and i3 are opposite of what we assumed initially.