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Counter-Strike: Source (2004)

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Consider a simple \( R C \) 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 \( V_{0} \) (i.e. charging continues for time \( T \gg R C \) ). In the process, some dissipation \( \left(E_{D}\right) \) 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 \( T \gg R C \). Then, the voltage is raised to \( \frac{2 V_{0}}{3} \) without discharging the capacitor and again maintained for a time \( T \gg R C \). 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. (2017 Adv.)
Figure 1
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Figure 2
In process 1 , the energy stored in the capacitor \( E_{C} \) and heat dissipated across resistance \( E_{D} \) are related by
(a) \( E_{C}=E_{D} \ln 2 \)
(b) \( E_{C}=E_{D} \)
(c) \( E_{C}=2 E_{D} \)
(d) \( E_{C}=\frac{1}{2} E_{D} \)
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