Correct Answer - Option 3 : Vat = QρL
The correct answer is Vat = QρL.
Formulae:
Formula or equation used to find electrical resistivity(ρ) =\(\ RA\over L\)
\(R= {\rho L \over A} \longrightarrow\)①
The equation used to find charge (Q) = \(Current(i) \times Time(t) \)
\(i={Q\over t}\longrightarrow\)②
From ohm's Law:
\(V=iR\)
\(R={V \over i} \longrightarrow\)③
Calculation:
Substitute equation ③ in equation ①:
\({V \over i}={\rho L \over A}\longrightarrow\)④
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.