"a circuit consists of a battery and two resistors connected in parallel. if the resistance in both resistors is doubled, and the current is kept constant, how does the voltage change? " why is the voltage doubled? ,

Let's call R the value of the resistance of the two resistors. In the first situation, the resistors are connected in parallel, so their equivalent resistance is given by:

which means:

And calling I the current in the circuit, the voltage is given by Ohm's law:


In the second situation, the resistance of each resistor is doubled: R'=2R. So, the equivalent resistance in this case is given by

which means

And the new voltage is given by:

which is twice the original voltage, so the voltage has doubled.