An infinite number of capacitors with capacit | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For capacitors connected in series,the equivalent capacitance $C_{eq}$ is given by the formula:$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} +

Vedclass · Accepted Answer

$0.75$

Vedclass · Answer

(C) For capacitors connected in series,the equivalent capacitance $C_{eq}$ is given by the formula:$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + ... + \infty$Substituting the given values:$\frac{1}{C_{eq}} = \frac{1}{C} + \frac{1}{4C} + \frac{1}{16C} + ... + \infty$$\frac{1}{C_{eq}} = \frac{1}{C} \left( 1 + \frac{1}{4} + \frac{1}{16} + ... + \infty ight)$The term in the bracket is an infinite geometric progression ($G$.$P$.) with the first term $a = 1$ and common ratio $r = \frac{1}{4}$.The sum of an infinite $G$.$P$. is given by $S_{\infty} = \frac{a}{1 - r}$.$S_{\infty} = \frac{1}{1 - 1/4} = \frac{1}{3/4} = \frac{4}{3}$.Therefore,$\frac{1}{C_{eq}} = \frac{1}{C} 	imes \frac{4}{3} = \frac{4}{3C}$.Thus,$C_{eq} = \frac{3}{4}C = 0.75C$.

An infinite number of capacitors with capacitances $C, 4C, 16C, ... \infty$ are connected in series. What is the equivalent capacitance of the combination in terms of $C$?

Similar Questions

Find the equivalent capacitance across $A$ and $B$ in $\mu F$.

If the equivalent capacitance between points $A$ and $B$ of the combination of capacitors shown in the figure is $6C$, then the capacitor $C^1$ is: (in $C$)

Three capacitors of $2\,\mu F$,$3\,\mu F$,and $6\,\mu F$ are joined in series,and the combination is charged by means of a $24\,V$ battery. The potential difference across the plates of the $6\,\mu F$ capacitor is.......$V$.

The equivalent capacitance between terminals $A$ and $B$ is:

Two capacitors are charged by a battery of $E$ volts as shown in the figure. What will be the ratio of the charges on these capacitors,$Q_1/Q_2$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module