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Resistors in parallel

In the circui...

Question

In the circuit diagram shown, the two resistance wires A and B are of same area of cross section and same material, but A is longer than B. Which ammeter $A_{1}$ or $A_{2}$ will indicate higher reading for current? The answer is $A_{x}$ then x is

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Solution

Resistance, $R = ρ \frac{l}{a}$
Since, $l_{a} > l_{b}$
Therefore, $R_{a} > R_{b}$
Potential contain resistance A=potential contain resistance B
$i_{a} R_{a} = i_{b} R_{b}$
$\frac{i_{b}}{i_{a}} = \frac{R_{a}}{R_{b}}$
$i_{b} > i_{a}$
Hence, $A_{2}$ is answer

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