But the current isn't "constant". The current is 'limited' so at Vc = 0 the current is limited to 50mA and the power supply output voltage is that determined by the capacitor's ESR and the limited current value. As the capacitor charges the current limit will stay effective until such time as the capacitor voltage is high enough to permit charge current below the current limitation value. From then onwards the charge current will decrease exponentially towards zero as the capacitor's voltage rises exponentially to the output voltage of the power supply. The only portion of the charge that may be described as linear is that area within the "limited' current phase due to the ESR of the capacitor