Question

Find out the potential difference between the points $x$ and $y$ in the figure.

• A. $7\text{V}$
  
• B. $10\text{V}$
  
• C. $17\text{V}$
  
• D. $12\text{V}$
  

Answer 1

The correct option is A $7\text{V}$


Given,
$E=24\text{V},R=2\Omega ,R_1=4\Omega ,R_2=6\Omega ,C_1=\frac{4}{3}\mu \text{F},C_2=4\mu \text{F}$

As the capacitor offers a very high resistance to the current in the steady state, so the current is prevented to pass through the capacitors.

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

$I_{net}=\frac{E}{R_{eq}}=\frac{24}{12}=2\text{A}$

Therefore, the terminal potential difference across $AB$ is,

$V_{AB}=24-I_{net}R=24-2\times 2=20\text{V}$

As the capacitors and resistance are in parallel, the potential difference of $20V$ is available to both the capacitors and the resistors.

$V_B-V_y=20\times \frac{6}{10}=12\text{V}......\left(i\right)$

$V_B-V_x=\frac{20\times \frac{4}{3}}{\frac{4}{3}+4}=5\text{V}......\left(ii\right)$

From Eqs.(i) and (ii),

$V_x-V_y=12-5=7\text{V}$

Hence, option (a) is the correct answer.