JEE MAIN - Physics (2021 - 24th February Morning Shift - No. 17)
Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :
4 : 1
1 : 2
2 : 1
1 : 4
Explanation
Given, C1 = C2 = C
When both capacitors are connected in series, their equivalent capacitance will be
$${1 \over {{C_s}}} = {1 \over C} + {1 \over C} = {2 \over C}$$
$$ \Rightarrow {C_s} = {C \over 2}$$
When both capacitors are connected in parallel, their equivalent capacitance will be
Cp = C + C = 2C
$$\therefore$$ The ratio of equivalent capacitance in series and parallel combination is
$${{{C_s}} \over {{C_p}}} = {{C/2} \over {2C}} = {1 \over 4}$$
$$\therefore$$ Cs : Cp = 1 : 4
When both capacitors are connected in series, their equivalent capacitance will be
$${1 \over {{C_s}}} = {1 \over C} + {1 \over C} = {2 \over C}$$
$$ \Rightarrow {C_s} = {C \over 2}$$
When both capacitors are connected in parallel, their equivalent capacitance will be
Cp = C + C = 2C
$$\therefore$$ The ratio of equivalent capacitance in series and parallel combination is
$${{{C_s}} \over {{C_p}}} = {{C/2} \over {2C}} = {1 \over 4}$$
$$\therefore$$ Cs : Cp = 1 : 4
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