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

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.