A series combination of n_1 capacitors,each o | vedclass

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

Question

(D) For the series combination of $n_1$ capacitors,each of capacitance $C_1$:Equivalent capacitance $(C_{eq})_1 = \frac{C_1}{n_1}$.Potential differenc

Vedclass · Accepted Answer

$\frac{9 C_1}{n_1 n_2}$

Vedclass · Answer

(D) For the series combination of $n_1$ capacitors,each of capacitance $C_1$:Equivalent capacitance $(C_{eq})_1 = \frac{C_1}{n_1}$.Potential difference $V_1 = 6 \ V$.Energy stored $U_1 = \frac{1}{2} (C_{eq})_1 V_1^2 = \frac{1}{2} \left( \frac{C_1}{n_1} \right) (6)^2 = \frac{18 C_1}{n_1}$.For the parallel combination of $n_2$ capacitors,each of capacitance $C_2$:Equivalent capacitance $(C_{eq})_2 = n_2 C_2$.Potential difference $V_2 = 2 \ V$.Energy stored $U_2 = \frac{1}{2} (C_{eq})_2 V_2^2 = \frac{1}{2} (n_2 C_2) (2)^2 = 2 n_2 C_2$.Given that the total energy is the same,$U_1 = U_2$:$\frac{18 C_1}{n_1} = 2 n_2 C_2$.Solving for $C_2$:$C_2 = \frac{18 C_1}{2 n_1 n_2} = \frac{9 C_1}{n_1 n_2}$.

Similar Questions

$1000$ small drops,each of radius $r$ and charge $q$,coalesce to form a single large drop. How many times greater is the potential of the large drop compared to the potential of a small drop?

Four capacitors of capacitance $10\,\mu F$ and a battery of $200\, V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed? (in $\mu C$)

In the circuit shown below, $C_1 = 10 \, \mu F$, $C_2 = C_3 = 20 \, \mu F$, and $C_4 = 40 \, \mu F$. If the charge on $C_1$ is $20 \, \mu C$, then the potential difference between $X$ and $Y$ is ......... $V$.

As shown in the figure,four capacitors each of capacitance $25 \, \mu F$ are connected. The voltmeter reads $200 \, V$. Find the charge on each plate of the capacitors.

Vedclass Test Series

Exam Paper Generator

Online Exam Module