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CBSE Class 12 Physics 2020 Outside Delhi Set 3 Paper

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Question : 10 of 13
Marks: +1, -0
You are given three capacitors of 2 μF,3 μF2\,\mu\mathrm{F}, 3\,\mu\mathrm{F} and 4 μF4\,\mu\mathrm{F}, respectively.
(a) Form a combination of all these capacitors of equivalent capacitance 133 μF\frac{13}{3}\,\mu\mathrm{F}.
(b) What is the maximum and minimum value of the equivalent capacitance that can be obtained by connecting these capacitors ?
Solution:  
(a) 2 μF2\,\mu\mathrm{F} and 4 μF4\,\mu\mathrm{F} capacitors are to be connected in series. So, the effective capacitor will be
Ceff=2×42+4=43 μFC_{\text{eff}} = \frac{2 \times 4}{2+4} = \frac{4}{3}\,\mu\mathrm{F}
With CeffC_{\text{eff}}, the 3 μF3\,\mu\mathrm{F} capacitor is to be connected in parallel. So, the equivalent capacitor will be
Ceqv=43+3=133 μFC_{\text{eqv}} = \frac{4}{3} + 3 = \frac{13}{3}\,\mu\mathrm{F}
(b) Maximum value of capacitance may be obtained by connecting the capacitors in parallel. In that case, the equivalent capacitance will be, (2+3+4)=(2+3+4)= 10 μF10\,\mu\mathrm{F}.
Minimum value of capacitance may be obtained by connecting the capacitors in series. In that case, the equivalent capacitance will be CSC_{S}.
1CS=12+13+14=1312\frac{1}{C_S} = \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{12}
∴CS=1213 μF\therefore C_S = \frac{12}{13}\,\mu\mathrm{F}
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