If I keep my charger plugged in while my phone is not connected, it does not heat up.
So, it is safe to keep the charger plugged while it is not connected to the phone? Will it draw current?
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Yes they will draw current and waste energy, but only very little.
I just measured two of my chargers I had lying around.
One used 0.104W and the other was around 0.09W with no load connected. Their power factor (\$\cos \phi\$) was pretty bad, around -0.33, so their VA was around 0.3VA. For these kind of powers we have no regulation in Germany which power factor has to be reached, but closer to 1 is always better.
I've used a Gossen Metrawatt Energy to measure that, just in case someone wonders.
So in a year one of them would use around 880Wh of energy for nothing. Sure if you put that in perspective to what I use over the whole year: around 1000kWh, it would only account to roughly 0,1%, so it doesn't matter much. It would cost me roughly 0.25€ per year.
I generally have a tendency to completely unpower any unused appliance, it saves energy from being wasted, but it also adds some safety. First the device may fail while I'm not around, which could be bad. And second if a thunderstorm comes around it may damage a lot more devices if I leave them all plugged in.
It depends entirely on the charger. Modern chargers are designed to NOT waste power when idle and consume extremely-low amounts of power if left connected to the AC mains.
Older chargers will run slightly warm when idle - this heat is wasted power.
Really old wall-warts with iron-core transformers waste relatively enormous amounts of energy as heat when idle. As a result, they are mostly banned these days and not allowed to be sold with new equipment any more.