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Note that the component does not limit the current to the value specified. All it does is try to maintain the output voltage. I have had a 78L05 output over 1A at 5V. The problem here is mostly the heat: exceeding the output current will cause the component to grow hot, to the point where it will burn you, or even destroy itself. It is therefore wise to know what the current consumption of your circuit will be, and choose the appropriate component.
As you can see from the schematic, there are two other components, both of them capacitors. At the input side I have a 10uF capacitor. This is to ensure that fluctuations in the input voltage are filtered out, as well as moments where the target circuit has peaks in the demand. It generally does not hurt to increase this capacitor: values up to 470uF are quite acceptable. Note that this capacitor has polarization and will therefore need to be inserted correctly. On the output side I usually suffice with a 0.1uF capacitor. Obviously it is possible to add a larger capacitor on this side too, but the ceramic capacitors are much faster than the electrolytic ones, and response time is generally more important. Apart from the one in the power circuit I also put the 0.1uF capacitors near all the current consuming components on the board. This is called "decoupling" and without them you might experience very strange behavior, as voltages might drop below operating requirements. If you feel that ceramic capacitors are not fast enough you could switch them for tantalum. However, tantalum capacitors have polarity, which is why I tend to avoid them.
In the circuit above I assume that it is hooked up to the mains using a wallwart. However, frequently I use batteries. As you need to exceed 6.6V my preferred method is a 9V battery. For high current applications this has to be a NiCd battery, as these give a lot more current than other batteries. This might seem odd, given that a 9V NiCd battery generally has "160mAh" written on it, which implies a small amount of current compared to a NiMH battery (300mAh). However, the C (charge/discharge rate) of a NiCd battery is 5C-10C, so it can actually provide 800mA-1600mA, whereas a NiMH usually doesn't exceed 0.5C, which means it would only provide 150mA. Of course, the NiCd battery only provides this power for 6-12 minutes, whereas the NiMH would last 2 hours. I'm not a fan of batteries that can not be recharged, because I sometimes forget to disconnect them which renders them useless, and because they are not good for the environment and difficult to dispose of.
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