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: 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