A 5 F capacitor is charged by being connected to a 3 ~V battery. The battery is then disconnected. If the resistance of the dielectric material between the capacitor plates is 10^9 , what is the charge remaining on the capacitor 1 ~h after it has been disconnected ?

Step-by-step solution

aligned & aligned T=R C & = (10^9 ) (5 10⁻⁶ ~F ) & =5 10^3 ~s aligned & = 5 10^3 ~s (60 ~s / min )(60 ~min / h ) = 5000 ~s 3600 ~s / h =1.4 ~h aligned The initial charge on the capacitor is aligned & Q₀=C V= (5 10⁻⁶ ~F )(3 ~V ) &= 1.5 10⁻⁵ C & After t=1 ~h , t / T=(1 ~h ) /(1.4 ~h ) &=0.71 & and aligned Q & =Q₀ e^ -t / T & = (1.5 10⁻⁵ C ) (e^ -0.71 ) & = (1.5 10⁻⁵ C )(0.49) & =7.4 10⁻⁶ C aligned aligned