Question

In the circuit shown a potential difference of $60V$ is applied across $AB$. The potential difference between the point $M$ and $N$ is :

• A. $10V$
• B. $15V$
• C. $20V$
• D. $30V$

Answer 1

The correct option is D $30V$

The equivalent capacitance for series combination of $(2C,C,2C)$ is $C_{eq}=(1/2C+1/C+1/2C{)}^{-1}=C/2$
As the capacitor C and $C_{eq}$ are in parallel so potential across each is equal to $V_{AB}=60V$
The equivalent charge $Q_{eq}=C_{eq}{V}_{AB}=\left(C/2\right)\left(60\right)=30C$
As 2C,C and 2C are in series so charge on each is equal to $Q_{eq}$
Potential across M and N $=$ potential across C in between M and N$=\frac{Q_{eq}}{C}=30C/C=30V$