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

Question

A cylindrical object of density $600\,\text{kg/m}^3$ and height $8$ cm is floating in a liquid of density $900\,\text{kg/m}^3$. Find height of cylinder inside liquid.

Answer 1

Step 1: Units of Inductance and Resistance.
Inductance $ L $ is in henries ($ H $), and resistance $ R $ is 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 unit of $ \frac{L}{R} $ is:\[\text{Unit of } \frac{L}{R} = \frac{\text{Unit of } L}{\text{Unit of } R} = \frac{\text{henry}}{\text{ohm}}.\]Using $ 1 \, H = \Omega \cdot s $:\[\frac{\text{henry}}{\text{ohm}} = \frac{\Omega \cdot s}{\Omega}.\]Simplification yields:\[\frac{\text{henry}}{\text{ohm}} = \text{seconds (s)}.\]Step 3: Final Answer.
The unit of $ \frac{L}{R} $ is:\[\boxed{\text{seconds (s)}}.\]

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

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