Question

For the circuit below, determine the current i2 if the nodal voltage va = 8 v, e2 = 17 v, r1 = 34 ω , r2 = 4 ω, and r3 = 38 ω .

Answer 1

The current i2 in the circuit is 0.2 A.

Step-by-step explanation:

To determine the current i2, we can use the nodal analysis method. First, we need to identify the nodes and assign node voltages. Then, we can write the nodal equations based on Kirchhoff’s current law (KCL). By solving these equations, we can find the value of i2.

Applying KCL at node a, we get:

(i1 - i2) / r1 + (va - e2) / r3 + (va - 0) / r2 = 0

Substituting the given values va = 8 V, e2 = 17 V, r1 = 34 Ω, r2 = 4 Ω, and r3 = 38 Ω into the equation and solving for i2, we find:

(8 - 17) / 38 + (8 - 0) / 4 = i2 / 34

-9/38 + 2 = i2 / 34

-9/38 + 76/38 = i2 / 34

67/38 = i2 / 34

i2 = (67/38) * 34

i2 ≈ 0.2 A

Therefore, the current i2 in the circuit is approximately 0.2 A.