Question

If \( L \) is the inductance and \( R \) is the resistance, then the unit of \( \frac{L}{R} \) is:

Hint:

The ratio \( \frac{L}{R} \) represents the time constant (\( \tau \)) in an \( RL \) circuit, which determines the rate of exponential decay of current or voltage.

Answer 1

Step 1: Units of Inductance and Resistance.
The inductance \( L \) is measured in henries (\( H \)), and the resistance \( R \) is measured in ohms (\( \Omega \)). The henry (\( H \)) is defined as: \[ 1 \, H = 1 \, \text{ohm-second} \, (\Omega \cdot s). \] Step 2: Derive the Unit of \( \frac{L}{R} \).
The expression \( \frac{L}{R} \) has the unit: \[ \text{Unit of } \frac{L}{R} = \frac{\text{Unit of } L}{\text{Unit of } R} = \frac{\text{henry}}{\text{ohm}}. \] Substituting \( 1 \, H = \Omega \cdot s \): \[ \frac{\text{henry}}{\text{ohm}} = \frac{\Omega \cdot s}{\Omega}. \] Simplify: \[ \frac{\text{henry}}{\text{ohm}} = \text{seconds (s)}. \] Step 3: Final Answer.
The unit of \( \frac{L}{R} \) is: \[ \boxed{\text{seconds (s)}}. \]