Question: I am trying to sniff packets using Wireshark.
But Wireshark collects packets of computers connected to my Router only.
If i know the IP address of a Computer , can i sniff the packets of that Computer ?
Or is there any way to sniff packets of Computers/devices that are not connected to my Router ?

Answer: 
Wireshark can collect packets on any interface that has those packets passing it. 

1. If you are running wireshark on a PC etc, then you will collect data from the machine it is running on to any other machine on the network.
2. If there is a hub in between that machine and any other machine you will see all of its traffic also. (hubs rarely exist in networking any more - unfortunately!)
3. If there is a switch between you and the other machine, you will only see broadcast traffic from the other machine. (if it is a managed switch, you can 'mirror' a port to allow wireshark to 'see' all the packets travelling across that port.
4. If you are running wireshark on a router, you will see all traffic passing over the interface that you have wireshark listening on. i.e. if you have a three port router, with lan1, lan2 and wan and listen on lan1, you will not see traffic going lan2 <> wan. but will see lan1 <> lan2 and lan1 <> wan1
5. If lan1 (as #4) is connected to a switch (as #3), the same will apply as #3
Wireshark will collect only packets that pass trough its Ethernet interface, so it depends on the LAN deployment.

For example, if the devices and the router connect to a **switch**, then Wireshark will collect only packets directed to the router, going out of the router and broadcast packets.

if the devices and the router connect to a **hub**, then Wireshark will collect every packet on the network.

If you are on a switch and need to monitor a device, there is a feature on enterprise switches that let you replicate all the traffic on one port on another port that we can call *monitoring port*. 

You can connect a PC with Wireshark on the *monitoring port* and collect every packet from / to that device.