In the given circuit,the charge Q_2 on the 2 | vedclass

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

Question

(A) The circuit consists of a capacitor $C$ in series with a parallel combination of $1 \ \mu F$ and $2 \ \mu F$ capacitors. The equivalent capacitanc

Vedclass · Accepted Answer

Vedclass · Answer

(A) The circuit consists of a capacitor $C$ in series with a parallel combination of $1 \ \mu F$ and $2 \ \mu F$ capacitors. The equivalent capacitance of the parallel part is $C_p = 1 \ \mu F + 2 \ \mu F = 3 \ \mu F$.The total capacitance of the circuit is $C_{eq} = \frac{C 	imes C_p}{C + C_p} = \frac{3C}{C + 3}$.The total charge supplied by the battery $E$ is $Q = C_{eq} E = \frac{3CE}{C + 3}$.This total charge $Q$ flows through the capacitor $C$ and then divides between the $1 \ \mu F$ and $2 \ \mu F$ capacitors in parallel.The charge $Q_2$ on the $2 \ \mu F$ capacitor is given by the charge division rule: $Q_2 = Q 	imes \left( \frac{2 \ \mu F}{1 \ \mu F + 2 \ \mu F} ight) = Q 	imes \frac{2}{3}$.Substituting the expression for $Q$: $Q_2 = \frac{2}{3} 	imes \left( \frac{3CE}{C + 3} ight) = \frac{2CE}{C + 3} = 2E \left( \frac{C}{C + 3} ight) = 2E \left( \frac{C + 3 - 3}{C + 3} ight) = 2E \left( 1 - \frac{3}{C + 3} ight)$.As $C$ increases from $1 \ \mu F$ to $3 \ \mu F$,the term $\frac{3}{C + 3}$ decreases,so $Q_2$ increases. The function $f(C) = \frac{2CE}{C + 3}$ represents a curve that is concave downwards (as the second derivative is negative),which matches the shape shown in graph $A$.

In the given circuit,the charge $Q_2$ on the $2 \ \mu F$ capacitor changes as $C$ is varied from $1 \ \mu F$ to $3 \ \mu F$. $Q_2$ as a function of '$C$' is given properly by:

Similar Questions

For the given circuit,find the charge on the $4\ \mu F$ capacitor in $\mu C$.

The potential difference between the points $P$ and $Q$ in the adjoining circuit will be :-

If the charge on the left plate of the $5\ \mu F$ capacitor in the circuit segment shown in the figure is $-20\ \mu C$,find the charge on the right plate of the $3\ \mu F$ capacitor in $\mu C$.

$A$ capacitor of $2\,\mu F$ capacitance is charged steadily from $0$ to $5\,C$. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to the charge on the capacitor?

Vedclass Test Series

Exam Paper Generator

Online Exam Module