A core should be chosen to work within the specific frequency as stated by the manufacturer. L1 is a powder core and has 32 turns of 0.75mm wire.

Variable Power Supply Circuit Diagram

The transformer has a 240V primary and has a secondary rated 24V at 2A. The bridge rectifier contains 4 diodes, their current rating needs to be high with respect to the transformers output current; if not the current may damage the diodes. C1 is the mainfiltering capacitor, the supply is further smoothed by the combination of L1 and C3. C2 and C4 are decoupling capacitors; their action further reduce ripple factor.

The regulator 78xxr, U1 utilizes the action of zener diode ZD1 which is in parallel with the potentiometer, R1. The tuning action of R1 produces a variable regulator output. The output voltage is variable from the regulator output to the regulator output plus the zener voltage. E.G. A 7805 regulator and 10V zener give an output adjustable from 5 to 15 Volts. The regulator may be changed to provide different output voltages as may the zener. the zener should be rated a minimum of 1.3 Watts.

T1 Transformer 10:1 Secondary 24V @ 2A
BR1 Bridge Rectifier 50V PIV 2A rating
U1 7805 N.B. This may be changed for different output voltages e.g. 7812 for higher output voltage
ZD1 15V zener @ 1.3W

Source:http://www.zen22142.zen.co.uk/Circuits/Power/vpsu.htm

T4 compairs the P1 slider voltage with the output voltage. Then the P1 slider voltage is 0,65 V higher than the adjusted voltage, T2 opens, which stops the T3-T5 Darlington base current.
The 18V, 1A transformer voltage must be filtered with B1 and C1. When the output current is more then 500 mA, the Bz1 starts the alarm (overloading). Bz1 must be a 24 V type, auto-oscillating.

2N3055 variable power supply schematic

This dc variable voltage power supply has not been tested.