how does a tank circuit work on a dc supply in a radio.

 

In fact, very well.

 

Your question is a bit unclear. The DC supply is filtered, but the filter setup is not referred to as a tank circuit.

In the receiver part, a tank circuit is used to select the frequency of interest. You might Google the term "parallel tank circuit" to see how one works.

 

Years ago, some ham-radio folk I hung out with used the term "pi-tank" to refer to the DC supply pi-network filter. A pi-network is a low-pass filter. When used in power supplies, the capacitors tend to shunt the AC to ground while blocking DC, and the coil tends to block AC while passing DC.

 

a tank circuit, a capacitor and inductor in parallel, will output a sine wave at it's resonant frequency (when Xl = Xc), when the dc supply is removed. basically the capacitor when discharging acts as the supply and causes the inductor to create a magnetic field. the inductor in turn, begins to collapse it's magnetic field inducing a current back into the capacitor, and this cycle continues back and forth, with damping amplitude over time due to circuit resistance.

imho what makes this tank allowed to operate is the fact that unlike the capacitor, the inductor reverses polarity between when it has created it's magnetic field and when it collapses. tanks are a lot more fun in ac circuits.

 

but how does a capacitor discharge when a dc supply is applied like in the case of a radio

 

a capacitor in a dc circuit will absorb the charge equal to the potential being applied to it. if a constant 6v were applied to a cap, after about 9 time constants (t = r x c), the voltage across the cap will reach and remain at 6v. only when the applied voltage changes, up or down, will the cap charge change.