A `100(mu)F` capacitor is joined to a 24 V battery through a `1.0 M(Omega)` resistor.Plot qualitative graphs (a) between current and time for the first 10 minutes and (b)between charge and time for the same period .

Explanation

Time constant = rC
` = 1 xx (10^6) xx 100 xx (10^-6) `
` 100 sec. `
` (a) q = VC (1-e^(-t/rc))`
` I = Current = dq/dt `
` = VC/rC .e^(-t/RC)`
` = V/r e^(-t/RC)`
` = 24 xx (10^-6) . E^(1/(t/100))`
` t = 10 min = 600 sec. `
` q = 24 xx (10^-4) xx (1- (e^-6))`
` = 23.99 xx (10^-4) `
` i = 24/(10^6) i/e = 5.9 xx (10^-8) amp. `
` (b) q = VC.(1-e^(-t/rc)).