Question

When a high resistance voltmeter is connected across a resistance $ R $ and its reading is $ 2\;V $ . An electric cell is sending the current of $ 0.4\;A $ in the electric circuit in which a rheostat is connected to vary the current. Find the resistance of the resistor.

Answer 1

Hint: To determine the resistance of the resistor, we use Ohm’s law. When a voltmeter is connected across a resistance, it tells the voltage drop caused by that resistance. A rheostat can vary the current across a circuit accordingly by adjusting the resistance caused by a rheostat.

Formula Used:
 $ V = IR $

Complete Step by step solution:
It is given in the question that the voltage across the resistance is, $ 2\;V $
The current reaching the resistance, $ 0.4\;A $
Ohm’s law states that the current flowing in a circuit is directly proportional to the potential difference between the two points on a circuit. This relation can be represented by the formula,
 $ V = IR $
where $ V $ is the voltage across the circuit.
 $ I $ is the current flowing in the circuit.
and $ R $ is the proportionality constant, known as resistance.
In the question, we can find the resistance of the resistor using Ohm’s law,
By putting the values,
 $ 2 = 0.4R $
Solving this, we get,
 $ R = \dfrac{2}{{0.4}} $
 $ R = 5\Omega $
Therefore the resistance of the resistor is $ 5\Omega $ .

Additional Information:
Resistance is the property of a material and depends on the length, cross-section area and the resistivity of a material. Resistance is directly proportional to the length of the resistor (wire) and is inversely proportional to the thickness or the cross-section area of the resistor. If a material is a good conductor of electricity, it will have low resistance. Similarly, if it is a bad conductor of electricity, it will have a high value of resistance. The SI unit for resistance is $ \Omega $ (Ohms).

Note:
A voltmeter is always connected in parallel with the device across which the voltage is to be determined, whereas an Ammeter is connected in series with a circuit. This is because the voltage across elements connected in parallel is the same whereas current across elements connected in series is the same.