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Column-1 gives three physical quantities...

Column-1 gives three physical quantities. Select the appropriate units for the choices given in column-II. Some of the physical quantities may have more than one choice.
`{:("Column-I",,"Column-II"),("Capacitance",,"ohm-second"),("Inductance",,"Coulomb"^(2)//"Joule"),("Magnetic induction",,"coulomb"//"volt"),(,,"newton"//"ampere metre"),(,,"volt-second"//"ampere"):}`

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To solve the problem of matching physical quantities with their appropriate units, we will analyze each quantity in Column-I and find the corresponding units in Column-II. ### Step-by-Step Solution: 1. **Capacitance**: - The formula for capacitance (C) is given by: \[ C = \frac{Q}{V} \] where \(Q\) is charge (in coulombs) and \(V\) is voltage (in volts). - Voltage can also be expressed as: \[ V = \frac{W}{Q} \] where \(W\) is work done (in joules). - Therefore, substituting for voltage, we have: \[ C = \frac{Q}{\frac{W}{Q}} = \frac{Q^2}{W} \] - The units of capacitance can be expressed as: - \(C = \frac{\text{Coulomb}}{\text{Volt}}\) (Option B) - \(C = \frac{\text{Coulomb}^2}{\text{Joule}}\) (Option C) - Thus, capacitance corresponds to options B and C. 2. **Inductance**: - The formula for inductance (L) can be derived from the relationship of electromotive force (emf): \[ \text{emf} = -L \frac{di}{dt} \] - Rearranging gives: \[ L = -\frac{\text{emf}}{\frac{di}{dt}} \] - Here, emf is measured in volts, \(di\) in amperes, and \(dt\) in seconds. Thus: \[ L = \frac{\text{Volt} \cdot \text{Second}}{\text{Ampere}} = \text{Volt-Second/Ampere} \] - Since \( \text{Volt/Ampere} = \text{Ohm} \), we can also express: \[ L = \text{Ohm} \cdot \text{Second} \quad \text{(Option A)} \] - Therefore, inductance corresponds to options A and A. 3. **Magnetic Induction**: - The magnetic induction (B) is defined in terms of force per unit charge: \[ B = \frac{F}{q} \] - In SI units, this can be expressed as: \[ B = \frac{\text{Newton}}{\text{Coulomb}} \quad \text{(Option D)} \] - Additionally, we can express it in terms of other units: \[ B = \frac{\text{Newton}}{\text{Coulomb}} \cdot \frac{1}{\text{Second}} = \frac{\text{Newton}}{\text{Coulomb} \cdot \text{Second}} = \frac{\text{Newton}}{\text{Ampere} \cdot \text{Meter}} \quad \text{(Option D)} \] - Therefore, magnetic induction corresponds to option D. ### Final Matching: - **Capacitance**: B, C - **Inductance**: A, A - **Magnetic Induction**: D ### Summary of Answers: - Capacitance: B, C - Inductance: A - Magnetic Induction: D
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