Question

Describe an activity to show the variation of resistance on length of wire

Answer 1

 3





Complete an electric circuit consisting of a cell, an ammeter, a nichrome wire of length l[say, marked (1)] and a plug key, as shown in Fig.5.


Fig.5 Electric circuit to study the factors on which the resistance of conducting wires depends

Now, plug the key. Note the current in the ammeter.Replace the nichrome wire by another nichrome wire of same thickness but twice the length, that is 2l [marked (2) in the Fig.5].Note the ammeter reading.Now replace the wire by a thicker nichrome wire, of the same length l [marked (3)]. A thicker wire has a larger cross-sectional area. Again note down the current through the circuit.Instead of taking a nichrome wire, connect a copper wire [marked (4) in Fig.5] in the circuit. Let the wire be of the same length and same area of cross-section as that of the first nichrome wire [marked (1)]. Note the value of the current.Notice the difference in the current in all cases.Does the current depend on the length of the conductor?Does the current depend on the area of cross-section of the wire used?

It is observed that the ammeter reading decreases to one-half when the length of the wire is doubled. The ammeter reading is increased when a thicker wire of the same material and of the same length is used in the circuit. A change in ammeter reading is observed when a wire of different material of the same length and the same area of cross-section is used. On applying Ohm’s law [Eqs. (5) – (7)], we observe that the resistance of the conductor depends (i) on its length, (ii) on its area of cross-section, and (iii) on the nature of its material. Precise measurements have shown that resistance of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to the area of cross-section (A). That is,

R α l(8)

and R α 1 / A(9)

Combining Eqs. (8) and (9) we get
R α l / A

Or R = ρ(l / A) (10)

where ρ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor. The SI unit of resistivity is Ω m. It is a characteristic property of the material.

Answer 2

refer to the image for the answer...