Question

Find the potential difference across point a and b in figure.

• A. $\left(\frac{{\epsilon }_1+{\epsilon }_2}{c_1+C_2}\right)C_1$
• B. $\left(\frac{{\epsilon }_1+{\epsilon }_2}{2c_1+C_2}\right)C_1$
• C. $\left(\frac{{\epsilon }_1+{\epsilon }_2}{3c_1+C_2}\right)C_1$
• D. $\left(\frac{{\epsilon }_1+{\epsilon }_2}{4c_1+C_2}\right)C_1$

Answer 1

Answer: (A)

The correct option is A $\left(\frac{{\epsilon }_1+{\epsilon }_2}{c_1+C_2}\right)C_1$

$V_1=\frac{Q}{C_1},V_2=\frac{Q}{C_2}$

$-{\epsilon }_1+V_1-{\epsilon }_2+V_2=0$

$\left({\epsilon }_1+{\epsilon }_2\right)=V_1+V_2$

${\epsilon }_1+{\epsilon }_2=\frac{Q}{C_1}+\frac{Q}{C_2}$

$Q=\left({\epsilon }_1+{\epsilon }_2\right)\left(\frac{C_1{C}_2}{C_1+C_2}\right)$

$V_2=\frac{Q}{C_2}$

$V_2=\left({\epsilon }_1+{\epsilon }_2\right)\left(\frac{C_1}{C_1+C_2}\right)$