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Q.

A and B are two square plates of same metal and same thickness but length of B is twice that of A. Ratio of resistances of A and B is

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a

4 : 1

b

1 : 2

c

1 : 4

d

1 : 1

answer is C.

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Detailed Solution

${R_A} = \frac{{\rho l}}{{l \times t}} = \frac{\rho }{t}\,\,and\,\,{R_B} = \frac{{\rho \times 2l}}{{2l \times t}} = \frac{\rho }{t}\,\,i.e.\frac{{{R_A}}}{{{R_B}}} = 1:1$

$R$ $A$ $$ $=$ $l$ $\times$ $tρl$ $$ $=$ $tρ$ $$ $and$ $R$ $B$ $$ $=$ $2$ $l$ $\times$ $tρ$ $\times$ $2$ $l$ $$ $=$ $tρ$ $$ $i$ $.$ $e$ $.$ $R$ $B$ $$ $R$ $A$ $$ $$ $=$ $1$ $:$ $1$

This shows the calculation of resistances $R_A$ $R$ $A$ $$ and $R_B$ $R$ $B$ $$ , proving that their ratio is 1:1.

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