Question

What is the unit of the ratio \(L/R\) where \(L\) is inductance and \(R\) is resistance?

• A. Ampere
• B. Second
• C. Ohm
• D. Volt

Hint:

For an RL circuit, the time constant is given by: \[ \tau = \frac{L}{R} \] It represents the time required for the current to reach about 63% of its final value.

Answer 1

The Correct Option is B

Concept: In electrical circuits, the ratio \( \frac{L}{R} \) appears frequently in circuits containing inductors and resistors, such as RL circuits. This ratio represents a quantity known as the time constant of the circuit. The time constant describes how quickly the current in an RL circuit increases or decreases when the circuit is switched on or off. Inductance \(L\) has the SI unit: \[ \text{Henry (H)} \] Resistance \(R\) has the SI unit: \[ \text{Ohm }(\Omega) \]

Step 1: Express the units in base form. \[ 1\,H = \frac{V \cdot s}{A} \] \[ 1\,\Omega = \frac{V}{A} \]

Step 2: Calculate the unit of \(L/R\). \[ \frac{H}{\Omega} = \frac{\frac{V\cdot s}{A}}{\frac{V}{A}} \] \[ = s \] Thus, the unit becomes second (s).

Step 3: Interpretation.
The ratio \(L/R\) gives the time constant of an RL circuit, which determines how fast the current reaches its steady value.