Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Each Capacitor in Figure Has a Capacitance of 10 µF. the Emf of the Battery is 100 V. Find the Energy Stored in Each of the Four Capacitors. - Physics

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Question

Each capacitor in figure has a capacitance of 10 µF. The emf of the battery is 100 V. Find the energy stored in each of the four capacitors.

Solution

Capacitors b and c are in parallel; their equivalent capacitance is 20 µF.

Thus, the net capacitance of the circuit is given by

`1/C_"net" = 1/10 + 1/20 + 1/10`

`⇒ 1/C_"net" = (2+1+2)/20 = 5/20`

`⇒ C_"net" = 4  "uF"`

The total charge of the battery is given by

`Q = C_"net"V = (4  "uF") xx (100  "V") = 4 xx 10^-4 C`

For a and d,

`q = 4 xx 10^-4  "C" and  "C" = 10^-5  "F"`

`therefore E = q^2/(2C) = (4 xx 10^-4)/(2 xx 10^-5)`

`⇒ E = 8 xx 10^-3 "J" = 8  "mJ"`

For b and c,

`q = 4 xx 10^-4 "C" and "C"_(eq) = 2"C" = 2 xx 10^-5  "F"`

`therefore V = q/C_(eq)  (4 xx 10^-4)/(2 xx 10^-5)  = 20 V`

`⇒ E = 1/2 CV^2`

`⇒ E = 1/2 xx 10^-5 xx 400`

`⇒ E = 2 xx 10^-3 "J" = 2  "mJ"`

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Solution Each Capacitor in Figure Has a Capacitance of 10 µF. the Emf of the Battery is 100 V. Find the Energy Stored in Each of the Four Capacitors. Concept: Energy Stored in a Capacitor.
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