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An electrical technician requires a capacitance of 2 μF in a circuit across a potential difference of 1 kV. A large number of 1 μF capacitors are available to him each of which can withstand a potential difference of not more than 400 V. Suggest a possible arrangement that requires the minimum number of capacitors.

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Class 12 Physics, CBSE and UP Board, Electrostatic Potential and Capacitance, Additional Exercise,Chapter-2 Exercise 2.23, NCERT Solutions for Class 12 Physics

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1 Answer

  1. Total required capacitance, C = 2 pF Potential difference, V = 1, kV = 1000 V

    Capacitance of each capacitor, C₁ = lμF

    Each capacitor can withstand a potential difference, V₁= 400 V

    Suppose a number of capacitors are connected in series and these series circuits are connected in parallel (row) to each other. The potential difference across each row must be 1000 V and potential difference across each capacitor must be 400 V.

    Hence, number of capacitors in each row is given as 1000/4 = 2.5

    Hence, there are three capacitors in each row.

    Capacitance of each row = 1/(1+1+1) = 1/3 μF

    Let there are n rows, each having three capacitors, which are connected in parallel. Hence, equivalent capacitance of the circuit is given as

    1/3 +1/3 + 1/3 +……..n terms = n/3

    However, capacitance of the circuit is given as 2 μF.

    Therefore n/3 =2 ,therefore n=6

    Hence, 6 rows of three capacitors are present in the circuit. A minimum of 6 x3 i.e.,18 capacitors are required for the given arrangement.

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