સ્તંભ\(- I\) એ ધાત્વીય સુવાહકમાં વહેતા પ્રવાહને અનુરૂપ ચોક્કસ ભૌતિક રાશિઓ આપે છે. સ્તંભ\(- II\) એ સંકળાયેલ વિદ્યુતીય રાશિઓ ધરાવતા અમુક ગાણિતીય સંબંધો દર્શાવે છે. સ્તંભ\(-I\) અને સ્તંભ\(-II\) ને યોગ્ય સંબંધોથી મેળવો.

સ્તંભ \(- I\) સ્તંભ\(- II\)

\((A)\) ડ્રિફટ વેગ \((P)\) \(\frac{m}{n e^{2} \rho}\)

\((B)\) વિદ્યુતીય અવરોધકતા \((Q)\) \(\mathrm{ne} v_{\mathrm{d}}\)

\((C)\) શિથીલન સમયગાળો \((R)\) \(\frac{\mathrm{eE}}{\mathrm{m}} \tau\)

\((D)\) પ્રવાહ ઘનતા \((S)\) \(\frac{E}{J}\)

A \((A)- (\mathrm{R}),(\mathrm{B})-(\mathrm{S}),(\mathrm{C})-(\mathrm{P}),(\mathrm{D})-(\mathrm{Q})\)
B \((A)-(R), (B)-(S), (C)-(Q), (D)-(P)\)
C \((A)-(R), (B)-(P), (C)-(S), (D)-(Q)\)
D \((A)-(R), (B)-(Q), (C)-(S), (D)-(P)\)

Verified Solution

Answer & Solution

Correct Answer

(A) \((A)- (\mathrm{R}),(\mathrm{B})-(\mathrm{S}),(\mathrm{C})-(\mathrm{P}),(\mathrm{D})-(\mathrm{Q})\)

Step-by-step Solution

Detailed explanation

\(J=\frac{I}{A}=n e v_{d}=\frac{n e^{2} \tau}{m} E=\sigma E=\frac{E}{\rho}\) \(V_{d}=\frac{e E}{m} I ; \rho=\frac{m}{n e^{2} \tau}\) or \(\rho=\frac{E}{J}, J=n e v_{d}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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સ્તંભ \(- I\)	સ્તંભ\(- II\)
\((A)\) ડ્રિફટ વેગ	\((P)\) \(\frac{m}{n e^{2} \rho}\)
\((B)\) વિદ્યુતીય અવરોધકતા	\((Q)\) \(\mathrm{ne} v_{\mathrm{d}}\)
\((C)\) શિથીલન સમયગાળો	\((R)\) \(\frac{\mathrm{eE}}{\mathrm{m}} \tau\)
\((D)\) પ્રવાહ ઘનતા	\((S)\) \(\frac{E}{J}\)