A constant voltage of $50 \mathrm{~V}$ is maintained between the points $A$ and $B$ of the circuit s

Question

A constant voltage of $50 \mathrm{~V}$ is maintained between the points $A$ and $B$ of the circuit shown in the figure. What is the current flowing through the $1 \Omega$ resistance?

Professor PC Thomas Classes · Answer

(a) : Let the potential at junction $C$ be $x$. Applying Kirchhoff's Current Law at $C$: $\frac{x-50}{1} + \frac{x-50}{3} + \frac{x-0}{2} + \frac{x-0}{4} = 0$. Multiplying by 12 gives $12x - 600 + 4x - 200 + 6x + 3x = 0 \Rightarrow 25x = 800 \Rightarrow x = 32 \mathrm{~V}$. The current through the $1 \Omega$ resistance branch is $I_1 = \frac{50 - x}{1} = \frac{50 - 32}{1} = 18 \mathrm{~A}$.