Q147 / 160 · TS EAMCET 2020 (11 Sep Shift 2) · Physics

Figure
Find potential difference points $A \& F$ and $F \&$ $B$.

  • A
    $V_{A F}=10.2 \mathrm{~V}, V_{F B}=15.4 \mathrm{~V}$
  • B
    $V_{A F}=22.3 \mathrm{~V}, V_{F B}=28.9 \mathrm{~V}$
  • Correct answer
    C
    $V_{A F}=28.5 \mathrm{~V}, V_{F B}=71.4 \mathrm{~V}$
  • D
    $V_{A F}=42.1 \mathrm{~V} V_{F B}=53.1 \mathrm{~V}$

Solution

The given circuit is Figure
The two capacitors of $5 \mu \mathrm{F}$ each are in parallel. So, their equivalent capacitance is $(5+5) 10 \mu \mathrm{F}$. Similarly, two $2 \mu \mathrm{F}$ capacitors are also in parallel. So, their equivalent capacitance is $(2+2) 4 \mu \mathrm{F}$. The circuit is now reduced to as shownFigure
In steady state, when all the capacitors are charged, no current flow in the circuit. So, potential across resistors is zero. As in parallel combination, potential is same in both wires $C D$ and $E G$, i.e. $100 \mathrm{~V}$. In series combination, the potential is divided between the capacitor in the inverse ratio of their capacitance, i.e. $\frac{V_{A F}}{V_{F B}}=\frac{4}{10}=\frac{2}{5} \text { or } 2: 5 \therefore V_{A F}=\frac{2}{7} \times 100=28.5 \mathrm{~V}$ and $V_{F B}=\frac{5}{7} \times 100=71.4 \mathrm{~V}$

Hence, the correct answer is option: 'C'.

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