Question

Which of the following is / are correct regarding a balanced wheatstone bridge shown below.

• A. Potential at point $X$ is equal to the potential at point $Y$
• B. $\frac{C_1}{C_2}=\frac{C_3}{C_4}$
• C. Equivalent capacitance across $\text{AB}$ is $\frac{C_1{C}_2}{C_1+C_2}+\frac{C_3{C}_4}{C_3+C_4}$
• D. Equivalent capacitance across $\text{AB}$ is $\frac{C_1{C}_3}{C_1+C_3}+\frac{C_2{C}_4}{C_2+C_4}$

Answer 1

Answer: (A), (B), (D)

Equivalent capacitance across $\text{AB}$ is $\frac{C_1{C}_3}{C_1+C_3}+\frac{C_2{C}_4}{C_2+C_4}$

In a wheatstone bridge no two capacitors are in series or parallel combination.

If potential at $X$ is same as potential at $Y$ we can say that the wheatstone's bridge is balanced.

Condition for a balanced wheatstone bridge is $$\frac{C_1}{C_2}=\frac{C_3}{C_4}$$When the potential difference across a capacitor is zero. The capacitor becomes redundant. Thus by removing the redundant capacitor makes the circuit as shown below


The equivalent capacitance $C_{eq}=\frac{C_1{C}_3}{C_1+C_3}+\frac{C_2{C}_4}{C_2+C_4}$

Hence, options (a) , (b) and (d) are the correct answers.