# How to determine resistance of a given wire by plotting a graph of potential difference versus current .

Experiment : To determine resistance of a given wire by plotting a graph of potential difference versus current .

Apparatus : A Resistance , a Voltmeter (0-3V) and an ammeter (0-3 V) of appropriate range , a battery (battery eliminator) , a rheostat , a meter bridge , one way key , connecting wires and a piece of sand paper .

Theory : According to Ohm’s Law , if I be the current flowing through a conductor and V be the potential difference across its end , then current flowing through a conductor is directly proportional to the potential difference across its end provided physical conditions such as temperature , pressure , length , area of cross section remains unchanged .

Mathematically ,

I ∝ V or , V ∝ I

V = I R

Where R is the constant of proportionality and is known as the resistance of the conductor

$\large \frac{V}{I} = R$

The Resistance of the conductor depends upon the nature of material , temperature and dimensions of conductor . In SI units , V is measured in volt , I is measured in ampere , R is measured in ohm .

To establish the current-voltage relationship , it is to be shown that the ratio V/I remains constant for a given resistance . The graph plotted between V and I must be a straight line . The constant ratio gives unknown value of resistance .

Procedure :

(i) Arrange the apparatus in proper manner .

(ii) Clean the ends of the connecting wire with the help of sand paper to remove the insulations if any .

(iii) While making connections ensure that +ve marked terminals of voltmeter and ammeter are joined towards the +ve terminal of the battery .

(iv) Find the least count of voltmeter and ammeter and determine the zero error .

(v) Plug the key (K) and slide the rheostat contact and check whether ammeter and voltmeter are working properly or not .

(vi) Adjust the sliding contact of the rheostat such that a small current passes through the resistance wire .

(vii) Note down the value of potential difference (V) from voltmeter and current (I) from ammeter .

(viii) Remove key (K) and allow it to cool , if heated .

(ix) Shift the rheostat contact slightly so that both ammeter and voltmeter show full divisions reading and not in fraction .

(x) Record the readings of voltmeter and ammeter

(xi) Repeat the procedure for four different settings of rheostat. Record your observations in a tabular form and find the ratio of V and I for each set of observations .

(xii) Plot a graph between potential difference (V) and current (I) taking V along X-axis and I along Y-axis . The graph comes to be a straight line .

(xiii) Cut the resistance wire at points where it leaves the terminals , stretch it and find its length by the metre scale .

Calculations :

(i) Find ratio of V and I for each set of observations .

(ii) Plot a graph between potential difference , V and current , I by taking V along X-axis and I along Y axis . The graph comesto be a straight line .

Resistance can be calculated as

$\displaystyle tan\theta = \frac{\Delta I}{\Delta V}$

$\displaystyle cot\theta = \frac{\Delta V}{\Delta I}$

$\displaystyle R = \frac{\Delta V}{\Delta I}$

$\displaystyle R = cot\theta$

Constant V/I gives resistance of the wire .

Resistance of the wire per cm = ….. Ω cm-1

Result : The Potential difference across the given wire varies linearly with current .

Resistance per cm of the wire is ……. Ω cm-1