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A capacitor of capacitance C fared is being charged from a.d.c supply of E volts through a resistance of R ohms, i) Show that most of the voltage across the capacitor builds up during the first time constant . Ii) Show that capacitor is almost fully charged after time equal to 5 time constants. |
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Answer» SOLUTION :The voltage developed across the capacitor during charging is : `V=V_0 (1- e^(-1//RC))` i) During the first time constant i.e., at t = RC seconds, `V= V_0 (1- e^(-RC//RC))` `=V_0 =(1-e^(-1))= 0.632 V_0 ` VOLTS Hence, most of the voltage (i.e. ,63.2%) builds up across the capacitor during first time constant : ii) After time equal to 5 time constant i.e., at t = 5 RC, `V= V_0 (1- e^(-5RC//RC))` =`V_0 (1-e^(-5))= 0.993 V_0` |
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