Question

Find the potential difference between points $x$ and $y$ in the given circuit,

• A. $\frac{8}{7}\text{V}$
  
• B. $2\text{V}$
• C. $\frac{3}{4}\text{V}$
  
• D. $\frac{4}{3}\text{V}$
  

Answer 1

The correct option is D $\frac{4}{3}\text{V}$


Distribution of potential at the junctions are shown below.


Since, no current passes through a capacitor in steady state.

Thus, at the steady state condition, current in the circuit is,

$I=\frac{V}{R}=\frac{24}{12}=2\text{A}$

Now, the potential difference across the $4\Omega$ resistor is,

$24-V_y=IR=2\times 4$

$\therefore V_y=16\text{V}$

Using KCL at junction $x$,

$4(V_x-4)+8(V_x-24)=0$

$\Rightarrow 3V_x=52$

$\Rightarrow V_x=\frac{52}{3}\text{V}$

$\therefore V_x-V_y=\frac{52}{3}-16=\frac{4}{3}\text{V}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.