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NEET 2005
Exam
NEET
Year
2005
Subject
Physics
Chapter
Capacitance

NEET 2005 · Physics · Capacitance

A network of four capacitors capacity equal C_1=C, C_2=2 C, C_3=3 C...

A network of four capacitors capacity equal C1=C,C2=2C,C3=3CC_1=C, C_2=2 C, C_3=3 C and C4=C_4= 4C4 C are conducted to a battery as shown in the figure. The ratio of the change on C2C_2 and C4C_4 is: A network of four capacitors capacity equal C_1=C, C_2=2 C, C_3=3 C and C_4= 4 C are conducted to a battery as shown in

Options

  1. A47\frac{4}{7}
  2. B322\frac{3}{22}
  3. C74\frac{7}{4}
  4. D223\frac{22}{3}

Correct answer

B. 322\frac{3}{22}

Step-by-step solution

Here C1,C2andC3C_1, C_2 and C_3 are in series. A network of four capacitors capacity equal C_1=C, C_2=2 C, C_3=3 C and C_4= 4 C are conducted to a battery as shown in
1C′=1C+12C+13C\frac{1}{C^{\prime}}=\frac{1}{C}+\frac{1}{2 C}+\frac{1}{3 C}1C′=6+3+26C=116C⇒C=6C11\begin{aligned} \frac{1}{C^{\prime}}& =\frac{6+3+2}{6 C}=\frac{11}{6 C}\\ \Rightarrow \quad C & =\frac{6 C}{11} \end{aligned}AlltheAll thecapacitors in branch number 1 is in series so the charge on each number capacitor is: Q^{\prime}=611\frac{6}{11}C V Also charge on capacitor C4C_4 is Q=4Q=4 V \therefore  Ratio =Q′Q=6CV11×4CV=322\text{ Ratio }=\frac{Q^{\prime}}{Q}=\frac{6 \mathrm{CV}}{11 \times 4 C V}=\frac{3}{22}
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