A combination of capacitors is set up as show | vedclass

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

Question

(A) The circuit consists of a $4 \mu F$ capacitor in series with a parallel combination of $3 \mu F$ and $9 \mu F$ capacitors. First,calculate the equ

Vedclass · Accepted Answer

$420$

Vedclass · Answer

(A) The circuit consists of a $4 \mu F$ capacitor in series with a parallel combination of $3 \mu F$ and $9 \mu F$ capacitors. First,calculate the equivalent capacitance of the parallel part: $C_p = 3 \mu F + 9 \mu F = 12 \mu F$. Now,the circuit branch has a $4 \mu F$ capacitor in series with $C_p = 12 \mu F$ across an $8 \ V$ source. The total equivalent capacitance of this branch is $C_{eq} = \frac{4 	imes 12}{4 + 12} = \frac{48}{16} = 3 \mu F$. The total charge flowing through this branch is $q = C_{eq} 	imes V = 3 \mu F 	imes 8 \ V = 24 \mu C$. This charge $q$ passes through the $4 \mu F$ capacitor. The voltage across the parallel combination $C_p$ is $V_p = V - V_{4\mu F} = 8 \ V - \frac{24 \mu C}{4 \mu F} = 8 \ V - 6 \ V = 2 \ V$. The charge on the $9 \mu F$ capacitor is $q_{9\mu F} = C_{9\mu F} 	imes V_p = 9 \mu F 	imes 2 \ V = 18 \mu C$. The total charge $Q$ is the sum of charges on the $4 \mu F$ and $9 \mu F$ capacitors: $Q = 24 \mu C + 18 \mu C = 42 \mu C = 42 	imes 10^{-6} \ C$. The electric field at a distance $r = 30 \ m$ is $E = \frac{kQ}{r^2} = \frac{9 	imes 10^9 	imes 42 	imes 10^{-6}}{30^2} = \frac{9 	imes 10^9 	imes 42 	imes 10^{-6}}{900} = 420 \ N/C$.

$A$ combination of capacitors is set up as shown in the figure. The magnitude of the electric field,due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4 \mu F$ and $9 \mu F$ capacitors),at a point distance $30 \ m$ from it,would equal ....... $N/C$.

Similar Questions

Plates $A$ and $B$ constitute an isolated,charged parallel-plate capacitor. The inner surfaces ($I$ and $IV$) of $A$ and $B$ have charges $+Q$ and $-Q$ respectively. $A$ third plate $C$ with charge $+Q$ is now introduced midway between $A$ and $B$. Which of the following statements is not correct?

Four identical capacitors are connected as shown in the diagram. When a battery of $6 \, V$ is connected between $A$ and $B$,the total charge stored is found to be $1.5 \, \mu C$. The value of $C_1$ is ........ $\mu F$.

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 ......... $V$.

In the network shown below,the charge accumulated in the capacitor in steady state will be ........... $\mu C$.

$A$ $4\ \mu F$ capacitor is charged to $80\ V$ and a $6\ \mu F$ capacitor is charged to $30\ V$. When they are connected together,the energy lost by the $4\ \mu F$ capacitor is ..... $mJ$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module