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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 capacitorif fullycharged to voltage V_(0) (i.e., charging continuesfor time T gt gt RC). In the process some dissipation(E_(D)) occurs across the resistance R. The amountof energyfinally stored in the fully charged capacitor is E_(c). Process 2 : In a different process the voltage is first set to (V_(0))/(3) and maintainedfor a charging time T gt gt RC. Then the voltage is raised to (2C_(0))/(3) without dischargingthe capacitorand again maintainedfor a time T gt gt RC. 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 processesare depictedin figure 2. In process2, total energy dissipatedacross the resistance E_(D) is : |
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Answer» `E_(D)=3((1)/(2)CV_(0)^(2))` |
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