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Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance2 Marks
Question
Three capacitors each of capacitance 9 pF are connected in series.
  1. What is the total capacitance of the combination?
  2. What is the potential difference across each capacitor if the combination is connected to a 120 V supply?
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Answer

Capacitance of each of the three capacitors, C = 9 pF
  1. Equivalent capacitance (C') of the combination of the capacitors is given by the relation,
$\frac{1}{\text{C}'}=\frac{1}{\text{C}}+\frac{1}{\text{C}}+\frac{1}{\text{C}}$

$=\frac{1}{9}+\frac{1}{9}+\frac{1}{9}=\frac{3}{9}=\frac{1}{3}$

$\therefore$ C' = 3µF

Therefore, total capacitance of the combination is 3µF.
  1. Supply voltage, V = 120 V
Potential difference (V) across each capacitor is equal to one-third of the supply voltage.

$\therefore\text{V}'=\frac{\text{V}}{3}=\frac{120}{3}=40\text{V}$

Therefore, the potential difference across each capacitor is 40 V.

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