# Evan's Space

## 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.

## N2007P1Q27 brightness of bulb

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.

## What do you mean by bulb rating of 240 V 60 W?

Power is the rate of work done or energy conversion.

So a bulb of power 60 W means that the bulb converts 60 J of electrical energy to light energy (and heat energy) in one second.

## Modification to ammeter to measure bigger current

Sensitivity of the ammeter means that how small a current the ammeter can measure.

Example, if the original set up is 0.2 A per division, and the modified set up can measure up to 0.1 A per division, so we say the latter one is more sensitive as it is able to measure smaller change in the currrent.