Match List – I with List – II.
| LIST I | LIST II | ||
|---|---|---|---|
| A. | Conductance | I. | \( \mathrm{A\,m^{-2}} \) |
| B. | Electrical conductivity | II. | mho |
| C. | Current density | III. | \( \mathrm{kg^{-1}\,s^{2}\,A} \) |
| D. | Mobility | IV. | mho \( \mathrm{m^{-1}} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-II, B-IV, C-I, D-III
Each quantity is matched through its defining relation and the unit that follows from it.
(A) Conductance — this matches (II) mho. Conductance is the reciprocal of resistance, \( G = 1/R \), so its unit is \( \Omega^{-1} \), called the mho (siemens).
(B) Electrical conductivity — this matches (IV) mho \( \mathrm{m^{-1}} \). Conductivity is the reciprocal of resistivity, \( \sigma = 1/\rho \), and \( \rho \) is measured in \( \Omega\,\mathrm{m} \), so \( \sigma \) is in \( \Omega^{-1}\mathrm{m^{-1}} \), that is mho \( \mathrm{m^{-1}} \).
(C) Current density — this matches (I) \( \mathrm{A\,m^{-2}} \). Current density is current per unit area, \( J = I/A \), so its unit is ampere per square metre.
(D) Mobility — this matches (III) \( \mathrm{kg^{-1}\,s^{2}\,A} \). Mobility is drift speed per unit field, \( \mu = v_d/E \). With \( \mathrm{V} = \mathrm{kg\,m^{2}\,s^{-3}\,A^{-1}} \):
\( \displaystyle \mu = \frac{\mathrm{m\,s^{-1}}}{\mathrm{V\,m^{-1}}} = \frac{\mathrm{m^{2}\,s^{-1}}}{\mathrm{kg\,m^{2}\,s^{-3}\,A^{-1}}} = \mathrm{kg^{-1}\,s^{2}\,A} \)