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Standard XII

Physics

Energy of a Capacitor

In Process 1,...

Question

In Process 1,the energy stored in the capacitor $E_{C}$ and heat dissipated across resistance $E_{D}$ are related by:

E_{C} = \frac{1}{2} E_{D}

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E_{C} = 2 E_{D}

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E_{C} = E_{D}

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E_{C} = E_{D} l n 2

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Solution

The correct option is C $E_{C} = E_{D}$
Potential difference $V$ across capacitor $C$ , and charge $q$ are related as
$V = \frac{q}{C}$
Final charge on the capacitor is $C V$
$W_{b} = C V^{2}$
$E_{C} = \frac{1}{2} C V^{2}$
$E_{D} = W_{b} - Δ E_{C} = C V^{2} - \frac{1}{2} C V^{2} = \frac{1}{2} C V^{2}$
Hence $E_{C} = E_{D}$

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Similar questions

Q. Consider a simple RC circuit as shown in Figure 1

Process 1 : In the circuit the switch

S

is closed at

t = 0

and the capacitor is fully charged to voltage

V_{e}

(i.e. charging continues for time

T >> R C

). In the process some dissipation (

E_{D}

) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is

E_{c}

.

Process 2 :

In a different process the voltage is first set to $\frac{V_{0}}{3}$ and maintained for a charging time T>>RC. Then the voltage is raised to $\frac{2 V_{0}}{3}$ without discharging the capacitor and again maintained for a time $T >> R C$ . The process is repeated one more time by raising the voltage to $V_{0}$ and the capacitor is charged to the same final voltage $V_{0}$ as in Process $1 .$

These two processes are depicted in Figure 2.

In Process 1, the energy stored in the capacitor $E_{c}$ and heat dissipated across resistance $E_{D}$ are related by

Q. The following facts are available:

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In Process 1,the energy stored in the capacitor EC and heat dissipated across resistance ED are related by:

The correct option is C EC=EDPotential difference V across capacitor C, and charge q are related as V=qCFinal charge on the capacitor is CVWb=CV2EC=12CV2ED=Wb−ΔEC=CV2−12CV2=12CV2Hence EC=ED

In Process 1,the energy stored in the capacitor $E_{C}$ and heat dissipated across resistance $E_{D}$ are related by: