Question

3. Let the energy stored "in the capacitor" be U. Show that U is given by the expression: U = 1/2 Q^2/C [Hint: The power P in the capacitor is given by P = dU/dt = IV where I = dQ/dt. This is a simple exercise on integration.] 4. Calculate the energy stored in the capacitor network in the figure below when the capacitors are fully charged and when the capacitances are C1=12.0?F, C2=2.0?F , and C3=4.0?F , respectively.

          3. Let the energy stored "in the capacitor" be U. Show that U is given by the expression: U = 1/2 Q^2/C

[Hint: The power P in the capacitor is given by P = dU/dt = IV where I = dQ/dt. This is a simple exercise on integration.]

4. Calculate the energy stored in the capacitor network in the figure below when the capacitors are fully charged and when the capacitances are C1=12.0?F, C2=2.0?F , and C3=4.0?F , respectively.

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3. Let the energy stored "in the capacitor" be U. Show that U is given by the expression: U = 1/2 Q^2/C

[Hint: The power P in the capacitor is given by P = dU/dt = IV where I = dQ/dt. This is a simple exercise on integration.]

4. Calculate the energy stored in the capacitor network in the figure below when the capacitors are fully charged and when the capacitances are C1=12.0?F, C2=2.0?F , and C3=4.0?F , respectively.

Added by Ines G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Nirmal P

02/23/2022

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We are given the power P in a capacitor as P = IV, where I = dQ/dt. We need to show that the energy stored in the capacitor, U, is given by the expression U = Q^2/2C. Then, we need to calculate the energy stored in a network of capacitors with given capacitances Show more…

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Let the energy stored "in the capacitor" be U. Show that U is given by the expression: U = 1/2 Q^2/C [Hint: The power P in the capacitor is given by P = dU/dt = IV where I = dQ/dt. This is a simple exercise on integration.] 4. Calculate the energy stored in the capacitor network in the figure below when the capacitors are fully charged and when the capacitances are C1=12.0μF,C2=2.0μF , and C3=4.0μF , respectively.

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00:01 In this question we will calculate the energy stored in a capacitor can be written as u is equal to q squared divided by 2c.

00:08 In part b we will calculate energy stored in a capacitor network.

00:13 So first of all we will solve the part a.

00:16 In part a we can write power p is equal to v multiplied with the i here v is the voltage, i is the flow of current.

00:27 So we can write power p is nothing but an energy.

00:30 Energy flow.

00:31 So del u divided by del t, here u is the energy.

00:36 So we can write del u divided by del t is equal to v multiplied with the del q divided by del t.

00:44 Here i is can be written as del q divided by del t if with del t cancels each other so we can write del u is equal to v multiplied with the del q.

00:56 In the case of capacitor we can write charge q is equal to c multiplied with the v from these values where voltage v can be written as q divided by c if we plug in the value of voltage v is equal to q divided by c we will get del u is equal to q divided by c del q if we integrate the both the terms u from del u from 0 to u del u can be written as if we integrate charge from 0 to q q ddl q divided by c from this value we will get u is equal to energy stored in capacitor is equal to q squared divided by 2c so this is the formula this is the formula that we have to prove that energy stored in a capacitor u is equal to q squared divided by 2c.

01:59 So here we have completed the first part and let we solve the second part.

02:05 In the second part we have given a network of three capacitors, c1, c2 and c3.

02:13 Value of c1, c2 and c3 is given in the question...

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