Question

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?

Answer 1

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