Question

Find Mesh currents i₁ and i₂ in the electric circuit of Fig.

Answer 1

Mark the nodes as shown in Fig.. 

Treat O as the reference node. 

From the dependent current source of 3i₁ amp between B and O, 

i₂ −i₁ = 3i₁ or 4i₁ = i₂ ...(a) 

V_B is related to V_A, V_C and the voltage across resistors concerned 

V_B = V_A −i₁ × 1 = 4 − i₁ V_B = V_C + i₂ × 2 = 3 + 2i₂ Hence 4 −i₁ = 3 + 2i₂ ...

(b) From equations (a) and (b) above, i₁ = 1/9 amp and i₂ = 4/9 amp

Substituting these, V_B = 35/9 volts