An initially uncharged capacitor C is fully charged by a device of constant emf connected in

An initially uncharged capacitor C is fully charged by a device of constant emf ξ connected in series with a resistor R.

(a) Show that the final energy stored in the capacitor is half the energy supplied by the emf device.

(b) By direct integration of i2R over the charging time, show that the thermal energy dissipated by the resistor is also half the energy supplied by the emf device.