Question

A narrow copper wire of length L and radius b is attached to a wide copper wire of length L and radius 2b, forming one long wire of length 2L. This long wire is attached to a battery, and a current is flowing through it. If the electric field in the narrow wire is E, the electric firld in the wide wire is.

Answer 1

As we know that Current in both wire will be same but both have different resistance as per

\(\mathrm{R} 1=\rho_{\mathrm{L} / \mathrm{A}}\)

\(\mathrm{R} 2=\rho_{\mathrm{L} / 4 \mathrm{~A}}\) (Because redius is double so cosssectional area will be four times)

So \(\mathrm{R} 1=4^{*}(\mathrm{R} 2)\)

So if current is same in both then voltage will be -

\(\mathrm{V} 1=4^{*}(\mathrm{~V} 2)\) (because \(\vee\) propostional \(\mathrm{R}, \mathrm{i}\) is same in all)

then-

\(E 1=4(E 2)\) (because E propostional \(V, r\) is same in all)

E2 \(=(E 1) / 4\) (Electric feild in wide wire)

Option E.