calculate the capacitance if the time taken for it to reach full charge in 5 minutes?
a capacitor charges through a 0.22 mega-ohms resistor.calculate the capacitance if the time taken for it to reach full charge is 5 minutes????
ans:- 2.7 * 10 to the power of -4 F
Given R=0.22MΩ, t=300s
The voltage of a capacitor charging through a resistor is given by:
v(t) = V*(1-exp(-t/RC))
And solving for capacitance C gives us:
C = -t/(R*ln(1-v(t)/V))
Because we use exponentials to model the circuit, there is a problem with the term “full charge” since it takes infinite time to reach 100%. However, since the capacitor was determined as fully charged by measuring equipment, we need to account for the measurement accuracy. Assuming typical 0.1% measurement accuracy, we have:
v(t)=0.999V
C = 197 μF
If we plug your answer value into the 1st equation above to find the voltage at 5 min, we get v(t)=0.995V. So it seems the problem assumes the measurement accuracy to be 0.5% (which is also common).
v(t) = 0.995V
C = 267 μF
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