The diagram shows three capacitors with their | vedclass

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

Question

(B) In a series combination,the charge $q$ on each capacitor is the same. Since $q = CV$,we have $V = \frac{q}{C}$,which implies $V \propto \frac{1}{C

Vedclass · Accepted Answer

$\frac{11}{3} 	ext{ V}$

Vedclass · Answer

(B) In a series combination,the charge $q$ on each capacitor is the same. Since $q = CV$,we have $V = \frac{q}{C}$,which implies $V \propto \frac{1}{C}$.Given capacitances are $C_1 = 1 \mu	ext{F}$,$C_2 = 2 \mu	ext{F}$,and $C_3 = 3 \mu	ext{F}$.The ratio of voltages across them is $V_1 : V_2 : V_3 = \frac{1}{C_1} : \frac{1}{C_2} : \frac{1}{C_3} = \frac{1}{1} : \frac{1}{2} : \frac{1}{3} = 6 : 3 : 2$.Let $V_1 = 6x$,$V_2 = 3x$,and $V_3 = 2x$.The breakdown voltages are $V_{1,max} = 2 	ext{ V}$,$V_{2,max} = 1 	ext{ V}$,and $V_{3,max} = 3 	ext{ V}$.For the capacitors not to break down,the voltage across each must not exceed its breakdown voltage:$1$) $6x \le 2 \Rightarrow x \le \frac{1}{3} 	ext{ V}$$2$) $3x \le 1 \Rightarrow x \le \frac{1}{3} 	ext{ V}$$3$) $2x \le 3 \Rightarrow x \le \frac{3}{2} 	ext{ V}$To satisfy all conditions,we must choose the smallest value,$x = \frac{1}{3} 	ext{ V}$.The total $emf$ $E = V_1 + V_2 + V_3 = 6x + 3x + 2x = 11x$.Substituting $x = \frac{1}{3} 	ext{ V}$,we get $E = 11 	imes \frac{1}{3} = \frac{11}{3} 	ext{ V}$.

The diagram shows three capacitors with their capacitances and their respective breakdown voltages. What should be the maximum value of the external $emf$ $(E)$ of the source such that no capacitor breaks down?

Similar Questions

Four capacitors,each of capacitance $8 \mu F$,are connected as shown in the figure. The equivalent capacitance between points $A$ and $B$ is: (in $\mu F$)

The difference between the equivalent capacitances of two identical capacitors connected in parallel and in series is $6 \mu F$. The value of the capacitance of each capacitor is (in $\mu F$)

What is the effective capacitance between points $X$ and $Y$ in $\mu F$?

Two capacitors of $1\,\mu F$ and $2\,\mu F$ are connected in series. The resultant capacitance will be ..... $\mu F$.

The effective capacitance between points $A$ and $B$ shown in the figure is (in $\mu F$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module