Ncert Exercises & Solutions

A metal rod of length 10 cm and a rectangular cross-section of $1~ \text {cm} \times 1/2~ \text {cm}$ is connected to a battery across opposite faces. The resistance will be:

1.	maximum when the battery is connected across $1~ \text {cm} \times 1/2~ \text {cm}$ faces.
2.	maximum when the battery is connected across $10~ \text {cm} \times 1~ \text {cm}$ faces.
3.	maximum when the battery is connected across $10~ \text {cm} \times 1/2~ \text {cm}$ faces.
4.	same irrespective of the three faces.

(a) Hint: The resistance of the rod will depend on the dimensions of the rod.

Step 1:

The resistance of the wire is given by:

R = ρ \frac{l}{A}

$R = ρ \frac{l}{A}$

Step 2:

For the greater value of R, l must be higher and A should be lower and it is possible only when the battery is connected across 1 cm x

(\frac{1}{2})

$(\frac{1}{2})$ cm (area of cross-section A).

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