Question

In the given circuit, in steady state, find the potential differences across points $\text{A}$ and $\text{B}$.

• A. $20\text{V}$
• B. $25\text{V}$
• C. $75\text{V}$
• D. $100\text{V}$

Answer 1

The correct option is B $25\text{V}$

As we know that, in steady state, current passes through the capacitors will be zero. For the given circuit, not even a single loop is being formed in the circuit in which current can flow. So we can solve this situation by using nodal analysis by distributing the potentials at the nodes as follows.

Note: At steady state, current through the capacitor remains zero, but potential difference across the capacitors is not zero.


Assuming potential of positive terminal of battery is $100\text{V}$.

Let potential at the node $x$ be $V_x$.

Here, the potential drop across the resistance will be zero, because $i=0$.

Using KCL at the node $x$ we get,

$3(V_x-100)+3(V_x-100)+1(V_x-0)+1(V_x-0)=0$

$\Rightarrow 8V_x=600$

$\Rightarrow V_x=75\text{V}=V_B$

The required potential difference is given by,

$V_A-V_B=100-75=25\text{V}$

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