Evan's Space

Wonders of Physics


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Ratio of resistiviities of wires X and Y – effect of diameter on cross-sectional area

The resistance of two wires X and Y are in the ratio of 2 : 1, their lengths are in the ratio 1 : 2 and their diameters are also in the ratio of 1 : 2.

What is the ratio of the resistivities of wires X and Y?

A     1:2     B     1:1     C     2:1     D     4:1

Solutions: Option B

Note that when the diameter of the wire doubles, the cross-sectional area increases by 4 times.

Comparing the resistances of both X and Y as shown below, the ratio of resistivities is 1:1.

Notes page17

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N2007P1Q27 brightness of bulb

Image

Solutions: Option B

As lamp X is thicker and shorter, these 2 factors make the resistance of X lower than Y.
Recall: Length increases, R increases & cross-sectional area increases, R decreases.
[R = pL/A]

As both bulbs are connected to the same mains, (assume 240V), the potential difference across the bulbs are 240 V.

Brightness of the bulb depends on power, P = IV or V2/R, since V is constant, I across X is higher due to lower R,
hence power of X is greater than power of Y, hence X is brighter.