NCERT science of 10th, in chapter electricity on page 205, there, a is line written:
a component use to regulate the current without changing the voltage source( simply voltage ) is called variable resistance(rheostat)
but according to the ohm's law voltage is directly proportional to the current
then how can a variable resistance is able to change the current?
do it voilates the ohm's law?
Best Answer
According to Ohm's law, the voltage across and current through a resistor are proportional.
If one places a variable resistance (rheostat) across a voltage source, the voltage across the rheostat is fixed.
By fixing the voltage across the rheostat, the current through becomes inversely proportional to the resistance:
$$i(R) = \frac{V}{R}$$
A circuit with just a voltage source and rheostat is uninteresting. Consider adding a light bulb in series.
With the rheostat set to $0 \Omega$, the light bulb produces full brightness.
The resistance of the bulb and rheostat are added in series. And, as before, the voltage across the series combination of rheostat and bulb is fixed.
Thus, as the resistance of the rheostat increases, the current through the bulb decreases.
However, we can also say, with equal validity, that the rheostat controls the voltage across the bulb.
If $R_P$ is the resistance of the rheostat and $R_B$ is the resistance of the bulb, the voltage across the bulb is given by voltage division:
$$V_B = V \frac{R_B}{R_P + R_B}$$
If this were the electrical engineering stack exchange site, I could add easily add a schematic of the circuit for clarity. Perhaps this question should be migrated.