Four capacitors and a battery are connected a | vedclass

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

Question

(D) The $7 \mu F$ and $3 \mu F$ capacitors are in series. Their equivalent capacitance $C_s$ is given by $\frac{1}{C_s} = \frac{1}{7} + \frac{1}{3} =

Vedclass · Accepted Answer

all of the above.

Vedclass · Answer

(D) The $7 \mu F$ and $3 \mu F$ capacitors are in series. Their equivalent capacitance $C_s$ is given by $\frac{1}{C_s} = \frac{1}{7} + \frac{1}{3} = \frac{10}{21} \mu F^{-1}$,so $C_s = 2.1 \mu F$.The charge on the series combination is $Q_2 = C_s 	imes V_s = (2.1 \mu F) 	imes (6 \ V + V_{3 \mu F})$. Since the potential drop across the $7 \mu F$ capacitor is $6 \ V$,the charge $Q_2$ on the $7 \mu F$ capacitor is $Q_2 = (7 \mu F) 	imes (6 \ V) = 42 \mu C$. This charge is the same for the $3 \mu F$ capacitor in series.The potential drop across the $3 \mu F$ capacitor is $V_3 = \frac{Q_2}{3 \mu F} = \frac{42 \mu C}{3 \mu F} = 14 \ V$. Thus,the total potential across the series branch is $V_{branch} = 6 \ V + 14 \ V = 20 \ V$.The charge on the $3.9 \mu F$ capacitor is $Q_1 = (3.9 \mu F) 	imes (20 \ V) = 78 \mu C$.The total charge from the battery is $Q = Q_1 + Q_2 = 78 \mu C + 42 \mu C = 120 \mu C$.The potential drop across the $12 \mu F$ capacitor is $V_{12} = \frac{Q}{12 \mu F} = \frac{120 \mu C}{12 \mu F} = 10 \ V$.The total e.m.f. of the battery is $E = V_{12} + V_{branch} = 10 \ V + 20 \ V = 30 \ V$.Since all statements are correct,the answer is $(D)$.

Four capacitors and a battery are connected as shown. The potential drop across the $7 \mu F$ capacitor is $6 \ V$. Then the:

Similar Questions

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 ........ $\mu F$.

Five similar condenser plates,each of area $A$,are placed at equal distance $d$ apart and are connected to a source of $e.m.f.$ $V$ as shown in the diagram. The charge on the plates $1$ and $4$ will be:

$A$ fully charged capacitor of capacity $C$ is discharged through a small resistance wire embedded in a solid block of specific heat $s$ and mass $m$ under thermally isolated conditions. If the temperature of the block is raised by $\Delta T$,the initial potential difference across the capacitor is

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

$A$ proton and a deuteron are initially at rest and are accelerated through the same potential difference. Which of the following is false concerning the final properties of the two particles?

Vedclass Test Series

Exam Paper Generator

Online Exam Module