Question 376: Electrostatics & Capacitance

Question

Figure shows a network of capacitors where the numbers indicates capacitances in  micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 $$\mu $$F is :

Accepted Answer

Equivalent capacitance of 6 $$\mu $$F and 12 $$\mu $$F is = $${{6 	imes 12} \over {12 + 6}}$$ = 4 $$\mu $$F
Equivalent capacitance of 4$$\mu $$F and 4$$\mu $$F
is = 4 + 4 = 8 $$\mu $$F
New circuit is $$ 	o $$
equivalent  capacitance of 1 $$\mu $$F and 8 $$\mu $$F is
= $${{1 	imes 8} \over {8 + 1}}$$ = $${8 \over 9}$$ $$\mu $$F
Equivalent capacitance of 8 $$\mu $$F and 4 $$\mu $$F is
= $${{8 	imes 4} \over {12}}$$ = $${8 \over 3}$$ $$\mu $$F
New circuit is $$ 	o $$
Equation capacitance of $${8 \over 9}$$ $$\mu $$F and $${8 \over 3}$$ $$\mu $$F is
= $${8 \over 9}$$ + $${8 \over 3}$$ = $${32 \over 9}$$ $$\mu $$F
$$ 	herefore $$   Equivalent capacitance of AB is
C
AB
= $${{C 	imes {{32} \over 9}} \over {C + {{32} \over 9}}}$$
Given that,
C
AB
= 1 $$\mu $$F
$$ 	herefore $$   1 = $${{C 	imes {{32} \over 9}} \over {C + {{32} \over 9}}}$$
$$ \Rightarrow $$   C + $${{{32} \over 9}}$$ = $${{32C} \over 9}$$
$$ \Rightarrow $$   $${{23C} \over 9} = {{32} \over 9}$$
$$ \Rightarrow $$   C = $${{32} \over {23}}$$ $$\mu $$F

Answer

$${{31} \over {23}}\,\mu F$$

Answer

$${{32} \over {23}}\,\mu F$$

Answer

$${{33} \over {23}}\,\mu F$$

Answer

$${{34} \over {23}}\,\mu F$$

Electrostatics & Capacitance

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 $\mu $F is :

Choose the correct answer: