 Does current or voltage of a circuit increase the intensity of the lamp on it
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# But if you make the current go up (assuming the rare circuits in which you control current directly rather than voltage) then the voltage will correspondingly go up as well.

Logically it is,

Increase in Voltage > Increase in current > Increase in heat dissipated in the coil > Increase in temperature of the coil > increase in intensity of the lamp.

However the above happens in a logical manner only in the design range of the lamp and the coil.

Because the coil of the lamp does not have the same resistance  when cold and when hot. There is some data on that here Page on fisica.unifi.ita
the concept is also explained here The filament lamp

So beyond the normal range it is not simple. At a low enough voltage the lamp may not emit any light. You can try this in an experiment connecting two lamps of unequal wattages in series where only one (with the lower wattage) will light though both are carrying the same current.

there is a test:
assum 2 lamps in the parallel and serial circuits . in the serial one we have voltage dropp but current increases, and we can see decreasing in the light intensity. but in parallel mode, the voltage rises and the current drops and you see that the lamps intensity increases.

It's technically the voltage which can be increased in a circuit. You cannot directly increase the current in a fixed circuit.
Thus, it is the voltage that will increase the intensity of the lamp connected in the circuit. However, for a fixed circuit, as you increase the voltage, the current will increase as well.