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

Concept: In an electrical circuit containing an inductor \(L\) and a resistor \(R\), the ratio \(L/R\) appears in the expression for the time constant of an LR circuit. The time constant determines how quickly the current grows or decays in the circuit. \[ \tau = \frac{L}{R} \] where \(L\) = inductance (Henry), \(R\) = resistance (Ohm).

Step 1: Determine units of \(L/R\). \[ \frac{L}{R} = \frac{\text{Henry}}{\text{Ohm}} \] Now, \[ 1\,\text{Henry} = 1\,\Omega \cdot s \] Therefore, \[ \frac{\text{Henry}}{\Omega} = \frac{\Omega \cdot s}{\Omega} = s \]

Step 2: Interpretation. Thus, the ratio \(L/R\) represents the time constant of the circuit, which has the unit of time. Hence, its SI unit is seconds.