Question

In the given circuit,the potential difference $(V_x-V_y)$ between the points $x$ and $y$ when capacitors reach steady state is___

• A. $-7V$
• B. $-18V$
• C. $+18V$
• D. $+7V$

Answer 1

The correct option is A

$-7V$

Given $E=24V,R=2\Omega ,R_1=4\Omega ,R_2=6\Omega ,C_1=\left(\frac{4}{3}\right)\mu F,C_2=4\mu F$.

As the capacitor offers a very high resistance to the current in the steady state, Current through the branch having capacitors is zero.

Now, the total resistance in the circuit is

$R_{eq}=R+R_1+R_2=2+4+6=12\Omega$

Hence, the net current in the circuit $=\frac{E}{R_{eq}}=\frac{24}{12}=2A$

Therefore, the terminal potential difference across is

$V_A-V_B=24-2\times 2=20V$

$V_A-V_y=\frac{4\times 20}{10}=+8V$

$V_A-V_x=\frac{4\times 20}{4\frac{4}{3}}=+15V$

$\therefore V_x-V_y=-7V$