Question

Two identical capacitors $1$ and $2$ are connected in series to a battery as shown in figure. Capacitor $2$ contains a dielectric slab of constant $K.Q_1$ and $Q_2$ are the charges stored in $1$ and $2$ . Now, the dielectric slab is removed and the corresponding charges are $Q_1^{\prime }$ and $Q_2^{\prime }$. Then

• A. $\frac{Q_1^{\prime }}{Q_1}=\frac{K+1}{K}$
• B. $\frac{Q_2^{\prime }}{Q_2}=\frac{K+1}{2}$
• C. $\frac{Q_2^{\prime }}{Q_2}=\frac{K+1}{2K}$
• D. $\frac{Q_1^{\prime }}{Q_1}=\frac{K}{2}$

Answer 1

Answer: (C)

Before the slab is removed, if
$C_1=C,C_2=KC$
$C_{\text{net }}=\frac{C_1{C}_2}{C_1+C_2}$
$=\frac{CKC}{C(1+K)}=\frac{KC}{K+1}$
$\therefore Q_1=Q_2=\frac{KCE}{K+1}$
After the slab is removed, $C_1=C_2=C$
$C_{\text{net }}=\frac{C}{2}$
$\therefore Q_1^{\prime }=Q_2^{\prime }=\frac{CE}{2}$
$\frac{Q_2^{\prime }}{Q_2}=\frac{CE/2}{KCE/(K+1)}=\frac{K+1}{2K}$