CBSE Class 12 Physics 2023 Delhi Set 3 Paper

Question : 12 of 14

Marks: +1, -0

Two conductors, made of the same material have equal lengths but different cross-sectional areas

A_1

and

A_2 (A_1>A_2)

. They are connected in parallel across a cell. Show that the drift velocities of electrons in two conductors are equal.

Solution:

When two conductors are connected parallel to a cell, then the potential difference across the two conductors will be same.

\;\;\text " So, "\;\;V_1\;=V_2

\;\text " Or, "\;\;I_1 R_1\;=I_2 R_2 \;\; \;\text " (from Ohm's law) "\;

\;\text " Or, "\;\;n e A_1 v_{d 1} R_1\;=n e A_2 v_{d 2} R_2

\;\text " Or, "\;\;A_1 v_{d 1} R_1\;=A_2 v_{d 2} R_2

\;\text " Or, "\; \;\; A_1 v_{d 1} ρ \;{l}/{A_1}\;=A_2 v d_2 ρ \;{l}/{A_2}

\;\; \;\; (\;\text " since "\; {\R}=ρ \;{l}/{A})

∴\; v_{d 1}\;=v_{d 2}

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