Determine 'V_o' and 'i' in the circuit shown in Fig.

Concept:

While applying KVL, the direction in which loop is to be traced is not important and following the sign convention is most important which is shown in below circuit

We can write an equation by using KVL around this closed path as,

-I1 R1 + E1 – I2 R2 – I3 R3 – I4 R4 + E2 = 0 (Required KVL equation)

i.e. E1 + E = I R1 + I2R2 + I3R3 + I4R4

Explanation:

Circuit diagram:

Applying KVL in loop:

- 12 + 4 i + 2vo - 4 + 6 i = 0

\(i = \frac{12+4-2V_o}{10}.....(1)\;\)

Also,

\(i = -\frac{v_o}{6}.....(2)\;\) 

Substituting ' i ' from equation (2) into (1).

\(\frac{-v_o}{6}=\frac{16-2v_o}{10}\;\)

2 vo = 16 x 6

v0 = 48 V.

From equation 2 

i = - v_o / 6 = - 48 / 6 = - 8 A