Relay Basics

Hello everyone !
I'm new to Arduino, and my first project had me reading up all about relays. I understood how the relay works regarding the NO, NC and COM connections. However the need for external power supply keeps bugging me. And I was reluctant to start off the connections because an image of me frying up my board keeps popping up at the back of my head.

So what I've understood so far is that -

Powering up the relays(JD-Vcc and Vcc), with Arduinos 5V is fine for a stand-alone operation as long as I dont exceed the current limit.

But if I was going to use Arduino for other purposes I should remove the jumper, and power up the relay by connecting the JD-Vcc to an external power supply ? Then Vcc of the relay side reamains unconnected ?
And its said that while doing so the ground of the Arduino should also be unconnected on the other side.
Is it so ?
If so, why ?

Thanks.

Take a look at this

The schematic shows how removing the jumper allows you to use a separate relay power supply.

OK, lets' see it actually in the discussion.

So this makes it clear that there are two sides to the relay board once the jumper is removed.

On the signal side, an input pulled LOW draws current from Vcc which needs to be connected to the Arduino 5 V terminal. You do not want to connect the GND terminal to Arduino ground unless you absolutely must.

On the right hand side, the relay is powered by the "JD-VCC" terminal and GND, preferably from a separate supply.

That said, you should be able to power it from the same 5 V regulated supply as the Arduino as long as you follow certain rules. The two power lines (Vcc and ground) from the relay module should run together from that module to the output terminals of the power supply, immediately adjacent to its output capacitor and the two power lines to the Arduino again should also run together from that module to the output terminals of the power supply. You are advised in addition, to place a 470 µF capacitor directly across the supply terminals of the relay board itself.

Thanks to both of you for your detailed response. I think I have the confidence to go ahead with it now, as soon as I get my external power supply of 5V ready.

Once again,
Thanks !