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Which of the following is the correct relation between potential difference ‘V’ across a metal wire of resistivity ‘ρ’, length ‘L’, and area of cross-section ‘A’ through which a charge ‘Q’ flows in ‘t’ seconds?
1. VρQ = AtL
2. VLt = AQρ
3. Vat = QρL
4. VQt = AρL

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Correct Answer - Option 3 : Vat = QρL

The correct answer is Vat = QρL.

Formulae:

Formula or equation used to find electrical resistivity(ρ) =\(\ RA\over L\)

\(R= {\rho L \over A} \longrightarrow\)

The equation used to find charge (Q) = \(Current(i) \times Time(t) \)

\(i={Q\over t}\longrightarrow\)

From ohm's Law:

\(V=iR\)

\(R={V \over i} \longrightarrow\)

Calculation:

Substitute equation ③ in equation ①:

\({V \over i}={\rho L \over A}\longrightarrow\)

Substitute equation② in equation ④:

\({Vt \over Q}={\rho L \over A}\)

Rearranging the above equation as:

VAt = QρL.

The Relation between potential difference ‘V’ across a metal wire of resistivity ‘ρ’, length ‘L’, and area of cross-section ‘A’ through which a charge ‘Q’ flows in ‘t’ seconds is:

VAt = QρL.

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