Question

What is the resistance of an electric arc lamp, if the lamp uses $20{\text{A}}$ when connected to a $220$ volt line?

Answer 1

We know that the relation between resistance, electric current and voltage is best described by ohm’s law which states that voltage across a conductor is directly proportional to the current flowing through the conductor when all physical conditions and temperature are constant.

Step by step Solution:
Given from the question, the Electric Arc lamp is using $20{\text{A}}$ and the voltage provided to it is $220$ volt. So, we can write,
Current flowing (I) = $20{\text{A}}$
Voltage (V) = $220$ volt
Now as per ohm’s law “the potential difference (voltage supplied) across a conductor is directly proportional to the current flowing through it”. Mathematically ohm’s law can be written in terms of very simple equation as below,
${\text{V = I}}\, \times {\text{ R}}$
Where V is the voltage across the conductor, I is the current flowing through it and R is the resistance offered by the conductor to the flow of current.
Since we need to find out the resistance of the electric arc lamp, above equation can be rearranged to calculate resistance as
${\text{R = }}\dfrac{{\text{V}}}{{\text{I}}}$
Substituting values of voltage (V) and current (I) in our equation
${\text{R = }}\dfrac{{220}}{{20}}\,\Omega$
Solving above equation we get, Resistance (R) = $11\,\Omega$
Therefore, resistance of an electric arc lamp (R) = $11\,\Omega$

Note: Please note that the S.I unit of resistance is ohm, which is based on the name of the scientist “Georg ohm” and is denoted by $\Omega$ . We should also keep in mind that ohm’s law is having some limitations as well and it can’t be applied to a unilateral network which allows the current to flow in just one direction such as diodes and transistors.