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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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N2010 P2Q12 Fuel gauge using variable resistor

Capture

Solutions:

View the video on how the gauge works.

<p><a href=”https://vimeo.com/138991946″>fuel guage using ammeter and variable resistor</a> from <a href=”https://vimeo.com/user10931667″>evantoh</a&gt; on <a href=”https://vimeo.com”>Vimeo</a&gt;.</p>

As the fuel level drops, the float which stays on the fuel surface will descend. The rod which is attached to the float will turn clockwise about the pivot X. As the rod turns, the resistance on the variable resistor increases. This increases the resistance of the circuit. Hence the current flowing through the circuit will decreases, causing the needle to deflect more to the left, indicating towards E (empty). Thus the reading on the fuel gauge decreases.

Capture2

Solutions:

(i) Both the fixed resistor and sensor are in series.

Total effective resistance Re = 5000 + 1000 = 6000 ohms

V = IR
12 = I x 6000
I = 0.0020 A

Hence potential across Y, V = IR (where I is constant in a series circuit)
= 0.0020 x 1000
= 2.0 V

(ii) When the temperature increases and the resistance of sensor Y decreases, the total effective resistance of the circuit decreases. Current flowing through the circuit increases.

Since V = IR, where the R of the fixed resistor is a constant 5000 ohms, as current I increases, the potential difference across the 5000 ohms resistor will increase.