Question

Unit of \(\mu_{0} \mathrm{C}\) is same as that of (A) current (B) resistance (C) electric charge (D) velocity

Short answer

The unit of the given expression \(\mu_{0} \mathrm{C}\) is tesla meter (Tm). However, none of the options provided in the question match the unit of the given expression. Therefore, the correct answer is not provided in this list.

Step-by-step solution

Identify the units of the given quantities

The given expression is \(\mu_{0} \mathrm{C}\). We need to find the units of this expression. The units for each constant and quantity are as follows: 1. \(\mu_{0}\) (magnetic permeability constant): \( Tm/A \) (tesla meter per ampere) 2. \(\mathrm{C}\) (coulombs): \(A \cdot s \) (ampere seconds)

Multiply the units to find the unit of the expression

Now that we've identified the units of each quantity, we will multiply the units of \(\mu_{0}\) and \(\mathrm{C}\) to find the unit of the given expression: Unit of \(\mu_{0} \mathrm{C}\) = (Unit of \(\mu_{0}\)) × (Unit of \(\mathrm{C}\)) Unit of \(\mu_{0} \mathrm{C}\) = \( (Tm/A) \times (As) \) Unit of \(\mu_{0} \mathrm{C}\) = \( Tm \)

Compare with the given options

The unit of the given expression, \(Tm\), is tesla meter. Now we'll compare this unit with the units of the options provided in the question: (A) Current: The unit of current is ampere (A), which doesn't match with tesla meter (Tm). (B) Resistance: The unit of resistance is ohm (Ω), which also doesn't match with tesla meter (Tm). (C) Electric charge: The unit of electric charge is coulomb (C), which is not equal to tesla meter (Tm). (D) Velocity: The unit of velocity is meter per second (m/s), which doesn't match with tesla meter (Tm). Since none of the given options have a unit that matches the unit of the given expression, we can conclude that the correct answer is not provided in this list.