JEE MAIN - Physics (2018 - 15th April Morning Slot - No. 26)
The equivalent capacitance between $$A$$ and $$B$$ in the circuit given below, is :
_15th_April_Morning_Slot_en_26_1.png)
$$2.4\,\mu F$$
$$4.9\,\mu F$$
$$3.6\,\mu F$$
$$5.4\,\mu F$$
Explanation
Given circuit :
_15th_April_Morning_Slot_en_26_2.png)
Simplified circuit.
_15th_April_Morning_Slot_en_26_3.png)
The equivalent capacitance between C and D = 2 + 5 + 5 = 12 $$\mu $$F
Equivalent capacitance between E and B = 4 + 2 = 6 $$\mu $$F
Now equivalent capacitance between A and B
$${1 \over {{C_{eq}}}}$$ = $${1 \over 6}$$ + $${1 \over 12}$$ + $${1 \over 6}$$ = $${5 \over 12}$$
$$ \Rightarrow $$$$\,\,\,\,$$ Ceq = $${12 \over 5}$$ = 2.4 $$\mu $$F
Note :
(1) When capacitors C1, C2, . . . .Cn are in parallel then equivalent capacitance
Ceq = C1 + C2 + . . . . + Cn
(2) When capacitor C1, C2 . . . . . . Cn are in series the equivalent capacitance
$${1 \over {{C_{eq}}}}$$ = $${1 \over {{C_1}}}$$ + $${1 \over {{C_2}}}$$ + . . . . . + $${1 \over {{C_n}}}$$
Simplified circuit.
The equivalent capacitance between C and D = 2 + 5 + 5 = 12 $$\mu $$F
Equivalent capacitance between E and B = 4 + 2 = 6 $$\mu $$F
Now equivalent capacitance between A and B
$${1 \over {{C_{eq}}}}$$ = $${1 \over 6}$$ + $${1 \over 12}$$ + $${1 \over 6}$$ = $${5 \over 12}$$
$$ \Rightarrow $$$$\,\,\,\,$$ Ceq = $${12 \over 5}$$ = 2.4 $$\mu $$F
Note :
(1) When capacitors C1, C2, . . . .Cn are in parallel then equivalent capacitance
Ceq = C1 + C2 + . . . . + Cn
(2) When capacitor C1, C2 . . . . . . Cn are in series the equivalent capacitance
$${1 \over {{C_{eq}}}}$$ = $${1 \over {{C_1}}}$$ + $${1 \over {{C_2}}}$$ + . . . . . + $${1 \over {{C_n}}}$$
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