Question

In the circuit shown in figure, (a) find the current in each branch (b) find the potential difference $V_{ab}$ of point $a$ relative to point $b$

Answer 1

(a) Current in the top branch is $0.8A$ from right to left. Current in the middle branch is $0.2A$ from left to right. Current in the bottom branch is $0.6A$ from left to right. (b) $V_{ab} = -3.2V$

Answer 2

Nodal analysis is applied by setting the potential of one junction to zero ($V_Y=0$). Kirchhoff's Voltage Law (KVL) is used for each branch to express the potential difference between junctions ($V_X - V_Y$) in terms of branch currents. Kirchhoff's Current Law (KCL) at the junction X ($I_1 + I_2 + I_3 = 0$) provides an equation to solve for the junction potential $V_X$. Once $V_X$ is known, branch currents are calculated. Then, potentials at points 'a' and 'b' are found by applying KVL along paths from a junction to these points. Finally, $V_{ab} = V_a - V_b$ is computed.