I have been quite sceptical of these gadgets prior to now, although admittedly I have never actually done the maths to work out what might or might not be achieveable with them.

My understanding is that they plug into the cigarette lighter / power socket in the car and top up the battery.

The max rated current through the power socket (roughly) is 10 amps. P=VI, so 12 x 10 = 120 J/s or 120W.

The starter motor of a car engine pulls 100-200 amps. Let's assume the engine needs a 5 second crank in the cold to make it start: that's 200 amps x 12 volts x 5 seconds = 12000 joules.

At 120W power delivery from the top-up charger, that's 12000 joules /120 joules/second = 100 seconds to return the energy from a single starting crank, which sounds reasonable.

But these products are usually marketed as rescue packs to get you going when you've left the lights on on and pancaked the battery. They often say they can "restore a flat battery in 15 minutes". So let's examine that:

A car battery is about 150 Ah (amp-hours). This means it can supply a current of 1 amp at about 12 volts for 150 hours; that's 1 x 12 x (150 x 3600) = 6,480,000 joules of energy.

To deliver this amount of energy back into the car battery via the cigarette lighter - at 120W - would therefore take 6,480,000 / 120 = 54,000 seconds or (divide by 3600 seconds per hour) = 15 hours!

After 15 minutes at 120W you could have transferred 120W x 15m x 60seconds per minute = 360,000 joules.

These are extreme case numbers that I have used, but all the same, you can see that one of these "get you started" rescue packs is not capable to restoring a car battery to the fully charged state from a fully discharged state.

Also, the current draw of 10A or higher from the recharge pack is quite high and likely to, ultimately, degrade the cells; so they are not going to survive too many discharge cycles like that.

I'd suggest, therefore, investing in a pair of jump leads, a mobile phone and an AA or RAC subscription as a more viable alternative.

[Can someone please check my reasoning / maths above, just in case my early-morning mental fog has caused me to make a mistake]