My Behringer Xenyx 1202 FX has "Balanced or Unbalanced Jacks". In addition the answer to this previous question reference both. What's the difference between the two types of Mono Jacks.
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If we're talking about 1/4" 'phone jack' patch cables, you can easily tell the difference by the number of conductors on the plug.
2-conductor cables are unbalanced, and can be identified by the "tip/sleeve" configuration of conductors on the plug. You can call this "TS" for short:
In contrast, a 3-conductor cable is balanced, and can be identified by the "tip/ring/sleeve" configuration, or "TRS":
An audio signal is a waveform provided by a change in voltage. That voltage needs to be relative to some other signal--most commonly a ground. Within a closed system you could use a single conductor to transmit this voltage relative to the the common ground of the system, but if you are connecting two different pieces of hardware, you need at minimum two conductors for a mono signal - one for ground, and one for voltage.
In a stereo signal, you need at minimum three conductors: one for ground, and then one for the voltage of each channel. When we are sending a signal relative only to ground, the line is referred to as unbalanced. Unbalanced lines are more susceptible to picking up interference, especially over large cable runs.
So, if we're talking about audio cables, the 1/4" TS can ONLY carry unbalanced mono signals. The 1/4" TRS is capable of carrying unbalanced stereo signals. However, the 1/4" TRS can ALSO be used for balanced mono signals. This requires a hot AND cold for the signal, IN ADDITION to ground.
If you examine a microphone XLR cable, you will notice that it too has three conductors. Microphones should ALWAYS use balanced cables due to the nature of the long cable runs. You can easily find 1/4" TRS to XLR adapters, since they are used for mono signals in the same way. Also keep in mind that if you plug a balanced cable into a jack that only accepts unbalanced connections, the signal will still work, but the entire line will be unbalanced since only two conductors are being used.