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-

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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.