Question

Which one of the following is equal to 1 mega ohm?
\[
  {\text{A}}{\text{. }}{10^3}{\text{ }}\Omega \\
  {\text{B}}{\text{. }}10{\text{ }}\Omega \\
  {\text{C}}{\text{. }}\dfrac{1}{{1005}}{\text{ }}\Omega \\
  {\text{D}}{\text{. }}{10^6}{\text{ }}\Omega \\
 \]

Answer 1

Hint: Here, we will proceed by defining the term resistance. Then, we will be discussing the factors which affect the resistance. Then, we will be mentioning its unit and will be seeing which one of the given options represents a value equal to 1 mega ohm.

Complete Step-by-Step solution:
An electron that passes through the wires and external circuit loads meets with resistance. Resistance is the impediment to flow of charge. The journey from terminal to terminal isn't a direct route for an electron. Rather, it is a zigzag direction, resulting from countless collisions with fixed atoms within the conductive material . The electrons are facing opposition or we can say hindrance to their movement. Although the electrical potential difference between the two terminals facilitates charge movement, resistance is what discourages it. The rate at which charge flows from terminal to terminal is the result of these two quantities having combined effect.
Firstly, the overall length of the wires can influence the resistance. The longer the wire, the greater the resistance it will have.
Secondly, the wire's cross-sectional area can affect the amount of resistance.h Wider wires have more cross-sectional area. That will result in lesser resistance present in the wider wire. Similarly, the wider the wire, the less resistance to the electric charge flow. If all other factors are the same, charge can pass through wider wires with greater cross-sectional areas than through thinner wires at higher rates.
Unit of resistance is ohm (\[\Omega \])
As we know that
\[{\text{A}}{\text{.}}\] 1 kilo ohm = 1000$ \times $1 \[\Omega \] = 1000 \[\Omega \] = \[{10^3}{\text{ }}\Omega \]
So, \[{10^3}{\text{ }}\Omega \] is equal to 1 kilo ohm not 1 mega ohm
Option A is incorrect.
\[{\text{B}}{\text{.}}\] 10 \[\Omega \] is equal to ten ohms not 1 mega ohm
Option B is also incorrect.
\[{\text{C}}{\text{.}}\] \[\dfrac{1}{{1005}}{\text{ }}\Omega \] represents \[\dfrac{1}{{1005}}\] ohms not 1 mega ohm
Option C is also incorrect.
\[{\text{D}}{\text{.}}\] 1 mega ohm = \[{10^6} \times {\text{1 }}\Omega = {10^6}{\text{ }}\Omega \]
So, \[{10^6}{\text{ }}\Omega \] is equal to 1 mega ohm
Hence, option D is correct.

Note- There is a clear relationship between the amount of resistance that the charge encounters and the length of the wire that it will traverse. After all, if resistance occurs as a result of collisions between the charge carriers and the wire atoms, then more collisions in a longer wire are likely to occur. More such collisions mean greater resistance.