Is it possible for one to connect a telephone cable to light up a light-bulb?
Answer
Theoretically - sort of yes.
In practice, not really.
The telephone system operator would be unhappy.
It is possible to connect a telephone cable to light up a light-bulb (assuming that you mean the cable from a "Central Office" telephone exchange or a PBX system) BUT
Doing so will probably disrupt telephone operation
Doing so will be against the terms of service for the line involved
The amount of power obtainable will be very very very small. An LED would be better and even that will be limited.
Central Office telephone systems use 50 volt supplies. Anything below about 100,000 ohms may cause problems and even that is marginal.
Available current at 100k would be 50/100k = 0.5 mA.
An LED would glow dimly at that current.
At 0.5 mA the available energy is V x I = 50 x 0.5 mA = 25 mW.
If you used a buck converter at say 80% efficint to power an LED you'd get about 25 mW x 80% = 20 mW.
For a white LED at say 3V that's about 7 mA
A high efficiency modern LED would be "quite bright" to the eye but not much good for illumination. ie 1 person could read a paperback book at good light level with this.
If you are prepared to draw as much power from a line as possible it will depend on how far you are away - but you may get tens of mA. Central Office systems are typically 50V. PBX may be 25V and possibly other voltages.
I forget typical feed resistances by a figure of 600 ohms comes to mind. You get maximum load power when you load to half voltage (maximum power transfer theorum) so at say 600 ohm load, 25V Power = V^2/R = 625/600 or about 1 Watt.
Quite possible less in practice and much less with distance.
Not so good for a bulb - good for many things with an LED.
BUT telephone circuits may shut the line circuit down if it sees this sort of loading.
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