A 2.0 capacitor is charged to a potential difference of 12 V and is subsequently connected to an uncharged 4.0 capacitor. Determine the heat produced during the charge transfer from one capacitor to the other.

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Capacitors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Capacitors

A 2.0 capacitor is charged to a potential difference of 12 V and is...

2.0 \mu\text{F}

capacitor is charged to a potential difference of

12 \text{ V}

and is subsequently connected to an uncharged

4.0 \mu\text{F}

capacitor. Determine the heat produced during the charge transfer from one capacitor to the other.
A 2.0 capacitor is charged to a potential difference of 12 V and is subsequently connected to an uncharged 4.0

A 2.0 capacitor is charged to a potential difference of 12 V and is subsequently connected to an uncharged 4.0

Options

A $48 \mu\text{J}$
B $96 \mu\text{J}$
C $192 \mu\text{J}$
D $144 \mu\text{J}$

Correct answer

B. $96 \mu\text{J}$

Step-by-step solution

Given:

C_1 = 2.0 \mu\text{F}

V_1 = 12 \text{ V}

C_2 = 4.0 \mu\text{F}

V_2 = 0 \text{ V}

The heat produced during the charge transfer is equal to the loss in electrostatic potential energy of the system:

\Delta H = \dfrac{1}{2} \dfrac{C_1 C_2}{C_1 + C_2} (V_1 - V_2)^2

Substituting the given values:

\Delta H = \dfrac{1}{2} \times \dfrac{2.0 \times 4.0}{2.0 + 4.0} \times (12 - 0)^2 \mu\text{J}

\Delta H = \dfrac{1}{2} \times \dfrac{8.0}{6.0} \times 144 \mu\text{J}

\Delta H = \dfrac{4}{6} \times 144 \mu\text{J} = 96 \mu\text{J}

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