Question

How do you verify that resistance of a conductor is proportional to the length of the conductor for constant cross section area and temperature?

Answer 1

Hint: To verify proportionality with length, vary length and take observations. The current decreases with increase in resistance if voltage applied is constant. For a constant voltage use a battery.

Complete Step-by-Step solution:
We can verify this with a simple experiment.
Circuit diagram:

Procedure:
As shown in the circuit diagram, connect an ammeter in series with the battery leaving a gap between P and Q.
Take metal wires of same material having different length and same cross sectional area. Connect the first wire between P and Q and measure the current using an ammeter. Note down this reading.
Now change wire and note down the current readings.
Repeat this procedure for 4-5 wires having different length.
Observation:
You will observe that the value of current decreases as we increase the length of wire. So from this we can say that as we are increasing the length the resistance is also increasing for given constant potential difference. Therefore we conclude that resistance of a conductor is proportional to the length of the conductor for constant cross section area and temperature.
Thus, \[R\propto L\]

Note: The resistance also varies with temperature and impurity in a given material. So it is very important to carry out this experiment in a constant temperature environment and also use wires of the same material. Choose an ammeter which shows noticeable change in readings when we change length of wire. If the ammeter is not showing noticeable change then change the ammeter having more least count. Since the metals have very small resistance current would be very high and the ammeter may show full scale deflection. To bring the deflection within range you can add additional high resistance in series with battery.