JEE MAIN - Physics (2019 - 11th January Evening Slot - No. 4)
Seven capacitors, each of capacitance 2 $$\mu $$F, are to be connected in a configuration to obtain an effective capacitance of $$\left( {{6 \over {13}}} \right)\mu F.$$ Which of the combinations, shown in figures below, will achieve the desired value
_11th_January_Evening_Slot_en_4_1.png)
_11th_January_Evening_Slot_en_4_2.png)
_11th_January_Evening_Slot_en_4_3.png)
_11th_January_Evening_Slot_en_4_4.png)
Explanation
Ceq = $${6 \over {13}}$$$$\mu $$F
Therefore three capacitors most be in parallel to get 6 in
$${1 \over {{C_{eq}}}} = {1 \over {3C}} + {1 \over C} + {1 \over C} + {1 \over C} + {1 \over C}$$
Ceq = $${{3C} \over {13}}$$ = $${6 \over {13}}$$$$\mu $$F
_11th_January_Evening_Slot_en_4_5.png)
Therefore three capacitors most be in parallel to get 6 in
$${1 \over {{C_{eq}}}} = {1 \over {3C}} + {1 \over C} + {1 \over C} + {1 \over C} + {1 \over C}$$
Ceq = $${{3C} \over {13}}$$ = $${6 \over {13}}$$$$\mu $$F
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