Question

What is the unit of the \(L/R\) ratio?

• A. Ohm
• B. Henry
• C. Seconds
• D. Coulomb

Hint:

In an LR circuit, the time constant is \(\tau = \frac{L}{R}\). Since \(1\,H = \Omega s\), the unit of \(L/R\) is seconds.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the physical unit of the ratio of Inductance (\(L\)) to Resistance (\(R\)).
Step 2: Key Formula or Approach:
In an RL circuit, the term \(L/R\) represents the inductive time constant (\(\tau\)). Dimensional analysis or the definition of Henry and Ohm can be used.
Step 3: Detailed Explanation:
1. The unit of Inductance (\(L\)) is Henry (\(H\)). Since \(e = -L(di/dt)\), \(1\ H = 1\ V \cdot s / A\).

2. The unit of Resistance (\(R\)) is Ohm (\(\Omega\)). Since \(V = IR\), \(1\ \Omega = 1\ V/A\).
Calculating the ratio:
\[ \text{Unit of } \frac{L}{R} = \frac{V \cdot s / A}{V / A} = s \]
This confirms that the ratio has the dimensions of time.
Step 4: Final Answer:
The unit of the \(L/R\) ratio is Seconds.