Find the equivalent capacitance between A and | vedclass

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

Question

(B) Let the capacitance of each parallel plate capacitor be $C = \frac{A\varepsilon_0}{d}$.From the circuit diagram,we can identify the arrangement of

Vedclass · Accepted Answer

$\frac{3A\varepsilon _0}{5d}$

Vedclass · Answer

(B) Let the capacitance of each parallel plate capacitor be $C = \frac{A\varepsilon_0}{d}$.From the circuit diagram,we can identify the arrangement of capacitors.There are four capacitors in total.Between $A$ and $C$,there is one capacitor of capacitance $C$.Between $C$ and $B$,there is one capacitor of capacitance $C$.Between $A$ and $C$ (via $D$),there are two capacitors in series,each of capacitance $C$,forming a branch with equivalent capacitance $\frac{C}{2}$.This branch is in parallel with the first capacitor between $A$ and $C$.So,the equivalent capacitance between $A$ and $C$ is $C_{AC} = C + \frac{C}{2} = \frac{3C}{2}$.Now,$C_{AC}$ is in series with the capacitor between $C$ and $B$.Therefore,the total equivalent capacitance $C_{eq}$ is given by:$\frac{1}{C_{eq}} = \frac{1}{C_{AC}} + \frac{1}{C} = \frac{1}{3C/2} + \frac{1}{C} = \frac{2}{3C} + \frac{1}{C} = \frac{2+3}{3C} = \frac{5}{3C}$.Thus,$C_{eq} = \frac{3C}{5} = \frac{3A\varepsilon_0}{5d}$.

Find the equivalent capacitance between $A$ and $B$.

Similar Questions

Ten capacitors are joined in parallel and charged with a battery up to a potential $V$. They are then disconnected from the battery and joined again in series. The potential of this combination will be ....... $V$.

Five capacitors are connected to a $DC$ potential of $100\,V$ as shown in the figure. Find the charge in the $10\,\mu F$ capacitor (in $\mu C$).

Three capacitors each of $6\,\mu F$ are available. The minimum and maximum capacitances which may be obtained are

The figure shows a network of capacitors where the numbers indicate capacitances in microfarads $(\mu F)$. The value of capacitance $C$ if the equivalent capacitance between points $A$ and $B$ is to be $1\,\mu F$ is:

Seven capacitors,each of capacitance $2\,\mu F$,are to be connected in a configuration to obtain an effective capacitance of $\left( \frac{6}{13} \right)\,\mu F$. Which of the combinations,shown in figures below,will achieve the desired value?

Vedclass Test Series

Exam Paper Generator

Online Exam Module