Question

Two identical condensers M and N are connected in series with a battery. The space between the plates of M is completely filled with a dielectric medium of dielectric constant $8$ and a copper plate of thickness $\frac{d}{2}$ is introduced between the plates of N ($d$ is the distance between the plates). Then potential differences across M and N are, respectively, in the ratio:

• A. $1:4$
• B. $4:1$
• C. $3:8$
• D. $1:6$

Answer 1

Answer: (A)

$1:4$

Let the capacitance of the condenser $M$ be $C$ and $N$ be $C^{\prime }$.

The new capacitance of the condenser $M$ will be, $C_M=\epsilon C_M=8C$

When a copper plate of thickness $d/2$ is inserted in between the capacitor N, effective distance between plates reduces to $d-d/2=d/2$.

Since, $C\propto \frac{1}{d},C^{\prime }=2C$

Since, the two condensers are connected in series, charge one each capacitor is same.

$\Rightarrow V_M:V_N=\frac{1}{C_M}:\frac{1}{C_N}=\frac{1}{8C}:\frac{1}{2C}$

$\Rightarrow V_M:V_N=1:4$