Question

The dimensions of $RC$ is

• A. square of time
• B. square of inverse time
• C. time
• D. inverse time

Answer 1

The Correct Option is C

To determine the dimensions of $RC$, we need to understand what $R$ and $C$ stand for in the context of physics, specifically within the realm of electrical circuits.

• R: Represents electrical resistance, and its SI unit is Ohm (\Omega). The dimensional formula for resistance is [ML^{2}T^{-3}I^{-2}].
• C: Represents capacitance, and its SI unit is Farad (F). The dimensional formula for capacitance is [M^{-1}L^{-2}T^{4}I^{2}].

The product $RC$ often emerges in analyzing RC circuits, where:

$RC = R \cdot C$

Let's substitute the dimensional formulas:

[RC] = [ML^{2}T^{-3}I^{-2}] \times [M^{-1}L^{-2}T^{4}I^{2}]

On multiplication:

• Mass terms: M^{1} \times M^{-1} = M^{0} (cancels out)
• Length terms: L^{2} \times L^{-2} = L^{0} (cancels out)
• Time terms: T^{-3} \times T^{4} = T^1
• Current terms: I^{-2} \times I^{2} = I^{0} (cancels out)

Therefore, the dimensional formula simplifies to:

[RC] = [T^1]

This shows that $RC$ has dimensions of time, confirming that the correct answer is time.

Thus, the dimensions of $RC$ is time.