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Chapter 11: Problem 1624

A variable condenser is permanently connected to a \(100 \mathrm{~V}\) battery. If capacitor is changed from \(2 \mu \mathrm{F}\) to \(10 \mu \mathrm{F}\). then energy changes is equal to (A) \(2 \times 10^{-2} \mathrm{~J}\) (B) \(2.5 \times 10^{-2} \mathrm{~J}\) (C) \(6.5 \times 10^{-2} \mathrm{~J}\) (D) \(4 \times 10^{-2} \mathrm{~J}\)

Short Answer

Expert verified
The change in energy when the capacitor is changed from $2 \mu \mathrm{F}$ to $10 \mu \mathrm{F}$ is \(\boldsymbol{4 \times 10^{-2} \mathrm{~J}}\).

Step by step solution

01

Calculate the energy for the first capacitor

The energy stored in a capacitor can be calculated using the following formula: \[E = \frac{1}{2}CV^2\] where C is the capacitance, and V is the voltage across the capacitor. For the first capacitor with a capacitance of 2 μF, the energy stored can be calculated as: \(E_1 = \frac{1}{2}(2\times10^{-6}\,\mathrm{F})(100\,\mathrm{V})^2\)
02

Calculate the energy for the second capacitor

Similarly, for the second capacitor with a capacitance of 10 μF, the energy stored can be calculated using the same formula: \(E_2 = \frac{1}{2}(10\times10^{-6}\,\mathrm{F})(100\,\mathrm{V})^2\)
03

Calculate the change in energy

Now, we will calculate the change in energy by finding the difference between the two energy values: ΔE = E₂ - E₁
04

Substitute the values and find the answer

Substitute the values of E₁ and E₂ in the formula, and calculate the change in energy: ΔE = \(\frac{1}{2}(10\times10^{-6}\,\mathrm{F})(100\,\mathrm{V})^2\) - \(\frac{1}{2}(2\times10^{-6}\,\mathrm{F})(100\,\mathrm{V})^2\) ΔE = \(4\times10^{-2}\,\mathrm{J}\) Hence, the change in energy is \(\boldsymbol{4 \times 10^{-2} \mathrm{~J}}\), which corresponds to option (D).

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Most popular questions from this chapter

A ball of mass \(1 \mathrm{gm}\) and charge \(10^{-8} \mathrm{c}\) moves from a point \(\mathrm{A}\), where the potential is 600 volt to the point \(B\) where the potential is zero. Velocity of the ball of the point \(\mathrm{B}\) is $20 \mathrm{~cm} / \mathrm{s}\(. The velocity of the ball at the point \)\mathrm{A}$ will be \(\ldots \ldots\) (A) \(16.8(\mathrm{~m} / \mathrm{s})\) (B) \(22.8(\mathrm{~cm} / \mathrm{s})\) (C) \(228(\mathrm{~cm} / \mathrm{s})\) (D) \(168(\mathrm{~m} / \mathrm{s})\)

Three charges \(2 q,-q,-q\) are located at the vertices of an equilateral triangle. At the centre of the triangle. (A) The Field is Zero but Potential is non - zero (B) The Field is non - Zero but Potential is zero (C) Both field and Potential are Zero (D) Both field and Potential are non - Zero

An electric circuit requires a total capacitance of \(2 \mu \mathrm{F}\) across a potential of \(1000 \mathrm{~V}\). Large number of \(1 \mu \mathrm{F}\) capacitances are available each of which would breakdown if the potential is more then \(350 \mathrm{~V}\). How many capacitances are required to make the circuit? (A) 24 (B) 12 (C) 20 (D) 18

A long string with a charge of \(\lambda\) per unit length passes through an imaginary cube of edge \(\ell\). The maximum possible flux of the electric field through the cube will be ....... (A) \(\sqrt{3}\left(\lambda \ell / \in_{0}\right)\) (B) \(\left(\lambda \ell / \in_{0}\right)\) (C) \(\sqrt{2}\left(\lambda \ell / \in_{0}\right)\) (D) \(\left[\left(6 \lambda \ell^{2}\right) / \epsilon_{0}\right]\)

Iwo points are at distances a and b \((a
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