A capacitor is a system of two conductors separated by an insulating medium. Capacitance of this system is determined purely geometrically, by the shapes, size and relative position of the conductors. The medium between the two conductors can be air or a dielectric. The way the dielectric is inserted accordingly by capacitance changes. Electric energy is stored in the capacitors. The capacitor can be connected in series or in parallel in an electric circuit.
An electrical technician required a capacitance of \( 2\,\mu\mathrm{F} \) in a circuit across a potential difference of 1 kV. A large no. of \( 1\,\mu\mathrm{F} \) capacitors are available to him each of which can withstand a potential difference of not more than 300 V. The minimum number of capacitor required for the arrangement will be.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 32
No capacitor may get more than 300 V, so the capacitors are first joined in series in a row to share the 1 kV, and then several such rows are joined in parallel to build up the capacitance.
Number in series in one row:
\( \displaystyle n \ge \frac{1000\,\mathrm{V}}{300\,\mathrm{V}} = 3.33 \;\Rightarrow\; n = 4 \)
Each capacitor then gets \( 1000/4 = 250\,\mathrm{V} \), which is within the limit. The capacitance of one row is
\( \displaystyle C_{\mathrm{row}} = \frac{1\,\mu\mathrm{F}}{4} = 0.25\,\mu\mathrm{F} \)
With \( m \) rows in parallel,
\( \displaystyle m \times 0.25\,\mu\mathrm{F} = 2\,\mu\mathrm{F} \;\Rightarrow\; m = 8 \)
\( \displaystyle N = n \times m = 4 \times 8 = 32 \)