To check if your TomTom is being charged,connect the charger ,power on the unit , tap the bottom right of the Driving view to get to the route summary screen. If the battery is being charged, the word Charging is shown under the battery symbol on the right. If you don't see the word Charging, the battery is either fully charged (indicated by a completely filled battery symbol) or it isn't receiving external power.
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The product of resistance and capacitance is referred to as the time constant. It determines rate of charging and discharging of a capacitor.
Phone will charge faster with a larger charging current. Charging current depends on voltage, so your home charger likely has a higher voltage and therefore a higher charging current.
It normally requres two coils of wire placed close to each other. The AC field on one will induce an AC field in the other. More chargers of portable equipment are using this method. It requires no physical contact, so reduces problems of poor contacts and can make the item more water proof.
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The voltage in your house is AC. It is in the form of a sine wave that goes positive and negative 60 times a second. To charge a battery you need DC so you do an AC to DC conversion and then apply the DC to the battery charging circuit that applies the correct charging current to the battery and checks on the state of the charge.