An RC circuit takes t = 2.5 ms to charge to 35% of its full charge after it weas connected to a battery, What is the total time
it takes for the capacitor of this curcuit to charge to 95% of the full charge?
1 answer:
Answer: time taken to charge to 95%
t = -5.80[ln(1-0.95)]
t = 17.38ms
Explanation:
For an RC Charging circuit
Where Vs
Vc = Vs (1 - e^(-t/RC))
Vc/Vs = 1 - e^(-t/RC)
-t/RC = ln(1 - Vc/Vs)
t = -RC[ln(1 - Vc/Vs)] and RC = k = -t/ln(1 - Vc/Vs)
Where ;
Vc = voltage across the capacitor
Vs = voltage supply
t = charging time = 2.5ms
k = RC = time constant.
Vc/Vs = 0.35
To calculate the time constant k;
k = -t/ln(1- Vc/Vs)
k = -2.5/ln(1-0.35)
k = 5.80ms
time taken to charge to 95%
t = -5.80[ln(1-0.95)]
t = 17.38ms
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