How can rheostat change the current without changing int voltage

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?

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.

• i could not understand the meaning of second paragraph – anni May 5 '14 at 15:16

as rheostat also has a considerable resistance which can be adjust according to one's choice. keeping this point in mind we can now understand the how rheostat can change the voltage across ends of resistor and current proportional to voltage. Rheostat is fixed in the circuit in series with the resistor. the total voltage (voltage across the ends of rheostat + voltage across the ends of resistor)remains the same in the entire circuit but across the ends of a resistor it would be different (less than the original voltage source or equal to that source) because some voltage is used up by the rheostat. And we know that current is directly proportional to voltage therefore current will also be adjustable by it.

**voltage and current directly proportional

rheostat fixes voltages

voltage and current now inversely proportional

if bulb involved: low rheostat, full brightness high rheostat, low brightness**

same explanation for microphones and other appliances