Question

Applying Kirchoff’s Current Law, determine current Is in the electric circuit of Fig. . Take V_o = 16 V.

Answer 1

Mark the nodes A, B, and O and the currents associated with different branches, as in Fig. 2.219 (p). 

Since V₀ = 16 V, the current through 8-ohm resistor is 2 amp. 

KCL at node B : 1/4 V₁ = 2 + i_a ...(a) 

KCL at node A : Is + i a = V₁/6 ...(b) 

Further, V_A = V₁, V_B = 16, V_B −V₁ = 4i_a ...(c) 

From (a) and (c), i_a = 1 amp. This gives V₁ −V_A = 12 volts, and I_S = 1 amp 

The magnitude of the dependent current source = 3 amp 

Check : Power from 1 amp current source = 1 × 12 = 12 W 

Power from dependent C.S. of 3 A = 3 × 16 = 48 W 

Sum of source-output-power = 60 watts 

Sum of power consumed by resistors = 2² × 6 + 1² × 4 + 2² × 8 = 60 watts 

The power from sources equal the consumed by resistors. This confirms that the answers obtained are correct.