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

From a supply of identical capacitors rated $8 \mu F, 250 V$,the minimum number of capacitors required to form a composite $16 \mu F, 1000 V$ capacitor is:

$A$ soap bubble is given a negative charge,then its radius

$A$ spherical drop of potential $2.5 \ V$ is formed from $125$ identical small drops. Find the potential of the large drop in $V$.

The given circuit shows two capacitors connected to a battery. After the capacitors are completely charged,the battery is removed and the capacitors are connected with plates of opposite polarity together. Then the charge on $2C$ and the energy lost in the process are respectively

In the circuit shown in the figure,the total charge is $750\, \mu C$ and the voltage across capacitor $C_{2}$ is $20\, V$. If $C_{3} = 8\, \mu F$,then the charge on capacitor $C_{2}$ is $....\mu C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module