Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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# A Capacitor of Capacitance 2⋅0 µF is Charged to a Potential Difference of 12 V. It is Then Connected to an Uncharged Capacitor of Capacitance 4⋅0 µF as Shown in Figure . - Physics

ConceptCapacitors and Capacitance

#### Question

A capacitor of capacitance 2⋅0 µF is charged to a potential difference of 12 V. It is then connected to an uncharged capacitor of capacitance 4⋅0 µF as shown in figure . Find (a) the charge on each of the two capacitors after the connection, (b) the electrostatic energy stored in each of the two capacitors and (c) the heat produced during the charge transfer from one capacitor to the other.

#### Solution

Charge on the 2 µF capacitor when it is not connected to the 4 µF capacitor is given by

q = C xx V = 12 xx 2 xx 10^-6

⇒ q = 24 xx 10^-6  "C"

(a) On connecting the capacitors, the charge flows from the 2 µF capacitor to the 4 µF capacitor.

Now, let the charges on the 2 µF and 4 µF capacitors be q1 and q2, respectively.

As they are connected in parallel, the potential difference across them is the same.

therefore V = q_1/C_1 = q_2/C_2

⇒ V = q_1/2 = q_2/4

⇒ q_2 = 2 q_1

The total charge on the capacitors will be the same as the initial charge stored on the 2 µF capacitor.

therefore q_1 + q_2 = 24 xx 10^-6

⇒ 3 q_1 = 24 xx 10^-6 C

⇒ q_1 = 8 xx 10^-6 C = 8  muC

⇒ q_1 = 2 q_1 = 16  muC

(b) Energies stored in the capacitors are given by

E_1 = 1/2 xx q_1^2/C_1 = 16  muJ

and

E_2 = 1/2 xx q_2^2/C_2 = 32  muJ

(c) Initial energy stored in the 2 µF capacitor is given by

E_i = 1/2 CV^2 = 1/2 xx (2 xx 10^-6) (12)^2

⇒ E_i = 144  muJ

Total energy of the capacitors after they are connected in parallel is given by

Ef = E1 + E2

⇒ Ef = 16 + 32 = 48 μJ

Heat produced during the charge transfer is given by

E = E_f - E_i

⇒ E = 144 - 48 = 96  muJ

Is there an error in this question or solution?

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Solution A Capacitor of Capacitance 2⋅0 µF is Charged to a Potential Difference of 12 V. It is Then Connected to an Uncharged Capacitor of Capacitance 4⋅0 µF as Shown in Figure . Concept: Capacitors and Capacitance.
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