Find the potential difference V_a - V_b betwe | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the potential at the bottom wire be $0 \, V$. Let the potential at node $X$ be $V_X$ and at node $a$ be $V_a$. Using nodal analysis at node $X

Vedclass · Accepted Answer

$\frac{12}{11} \, V$

Vedclass · Answer

(A) Let the potential at the bottom wire be $0 \, V$. Let the potential at node $X$ be $V_X$ and at node $a$ be $V_a$. Using nodal analysis at node $X$: $(V_X - 12) 	imes 2 + (V_X - 0) 	imes 4 + (V_X - V_a) 	imes 2 = 0$ $2V_X - 24 + 4V_X + 2V_X - 2V_a = 0$ $8V_X - 2V_a = 24 \implies 4V_X - V_a = 12 \implies V_X = \frac{12 + V_a}{4} = 3 + \frac{V_a}{4}$ Using nodal analysis at node $a$: $(V_a - V_X) 	imes 2 + (V_a - 0) 	imes 4 = 0$ $2V_a - 2V_X + 4V_a = 0$ $6V_a = 2V_X \implies V_X = 3V_a$ Equating the two expressions for $V_X$: $3V_a = 3 + \frac{V_a}{4}$ $12V_a = 12 + V_a$ $11V_a = 12 \implies V_a = \frac{12}{11} \, V$ Since $V_b = 0 \, V$,the potential difference $V_a - V_b = \frac{12}{11} \, V$.

Find the potential difference $V_a - V_b$ between the points $a$ and $b$ shown in the figure.

Similar Questions

When two identical capacitors are charged individually to different potentials and connected in parallel to each other,after disconnecting them from the source:

The separation between the plates of an isolated charged parallel plate capacitor is increased. Which of the following quantities will change?

Two particles of equal mass $m$ have charges $+q$ and $+4q$. If they are accelerated through the same potential difference $V$,the ratio of their velocities $\frac{v_A}{v_B}$ is:

Two capacitors of $3\,pF$ and $6\,pF$ are connected in series and a potential difference of $5000\,V$ is applied across the combination. They are then disconnected and reconnected in parallel. The potential between the plates is

Three uncharged capacitors of capacitances $C_1$,$C_2$,and $C_3$ are connected as shown in the figure. If $A$,$B$,and $C$ are at potentials $V_1$,$V_2$,and $V_3$ respectively,then the potential at point $O$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module