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There are lots of unshielded, twisted pair cables... but I bet you want to look into something to do with networking.
\(Welcome~to~Open~Study~!\) Unshielded twisted pair (UTP) cables are widely used in the computer and telecommunications industry. UTP cable is not surrounded by any shielding. It is the primary wire type for telephone usage and is very common for computer networking, especially as patch cables or temporary network connections due to the high flexibility of the cables @munal https://en.wikipedia.org/wiki/Twisted_pair
well unshielded is obvious, but the purpose of a balanced pair is that you typically use a balanced line of two wires with equal impedance in close proximity so that external noise affects both in a similar way; typically, one wire is hot and carries the signal whereas the other is grounded to 0V so its transients capture the noise during transmission and when fed into a differential amplifier the noise can be subtracted.
but the problem often occurs that nearby sources of noise tend to affect one (closer) wire more more strongly, so this results in noise levels differing between the two wires and thus a terminal differential amplifier is unable to subtract out the noise as effectively. to remedy this the pair is twisted about itself so that each wire nearly alternate in position closest to any external sources of noise to prevent this asymmetry
unshielded twisted pair, a popular type of cable that consists of two unshielded wires twisted around each other. Due to its low cost, UTP cabling is used extensively for local-area networks (LANs) and telephone connections. UTP cabling does not offer as high bandwidth or as good protection from interference as coaxial or fiber optic cables, but it is less expensive and easier to work with.
the pairs are typically unshielded just because of flexibility requirements, and the most common example is probably the Cat5 cables used for Ethernet over twisted pair
note that in many applications differential signaling is used where each wire carries the signal only inverted relative to the other, as this helps reduce the problem of cross-talk in comparison to the one-hot-one-cold balanced pair scheme
fun fact: because the point of balanced pairs is common-mode rejection, the absolute voltages do not matter -- you can carry data pulses on a DC voltage of say 5V and then have the 2nd wire carry 5V as well and extract everything correctly; in schemes that allow transmitting power and data on the same line, typically some form of inductive or capacitive coupling is done so that the DC bias does not affect the signal and then the common-mode can be used for power