To Determine Resistance Per Cm Of A Given Wire By Plotting A Graph Of Potential Difference Versus Current. - Practice Questions & MCQ

Aim-
To determine resistance per cm of a given wire by plotting a graph of potential difference versus current.

Apparatus-
A resistance wire, a voltmeter (0-3) V and an ammeter (0-3) A of appropriate range, a battery (battery
eliminator), a rheostat, a meter scale, one-way key, connecting wires and a piece of sandpaper.

Theory-

According to Ohm's law the current flowing through a conductor is directly proportional to the potential difference across its ends provided the physical conditions (temperature, dimensions, pressure) of the conductor remain the same.

If I be the current flowing through a conductor and V be the potential difference across its ends, then according to, Ohm's Law,

$
\begin{aligned}
& I \propto V \\
& V \propto I \\
& \text { or } V=R I
\end{aligned}
$

where R is the constant of proportionality. It is known as the resistance of the conductor.
So we can use

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

R depends upon the nature of the material, temperature, and dimensions of the conductor.
In S.I. units, the potential difference V is measured in volt and the current lin ampere, the resistance R is measured in ohm.
(1) To establish the current-voltage relationship, it is to be shown that the ratio $\frac{V}{I}$ remains constant for a given resistance, therefore a graph between the potential difference $(\mathrm{V})$ and the current $(\mathrm{l})$ must be a straight line.
(2) The constant ratio gives unknown value of resistance, $\left(\frac{V}{I}=R\right)$

Circuit Diagram-

 Procedure-
1. Arrange the apparatus in the same manner as given in the arrangement diagram.
2. Clean the ends of the connecting wires with sandpaper to remove the insulations, if any.
3. Make neat, clean and tight connections according to the circuit diagram. While making connections ensure that + ve marked terminals of voltmeter and ammeter are joined towards the + ve terminal of the battery.
4. Determine the least count of voltmeter and ammeter, and also note the zero error, if any.
5. Insert the key K, slide the rheostat contact and see that ammeter and voltmeter are working properly.
6. Adjust the sliding contact of the rheostat such that a measurable current passes through the resistance coil or the resistance wire.
7. Note down the value of potential difference $V$ " from voltmeter and current I from ammeter.
8. Shift the rheostat contact slightly so that both ammeter and voltmeter show full division readings and not in the fraction.

9. Record the readings of the voltmeter and ammeter.

Note- In the case of battery eliminator, follow these steps:
Turn the knob at 2 V in a battery eliminator and put the constant point in rheostat at the fixed position. Now record the reading in voltmeter and ammeter. Without disturbing the rheostat, turn the knob of battery to a different voltage such that 4,6,8,10 and 12 Volts and record corresponding readings in voltmeter and ammeter.
10. Take at least five sets of independent observations.
11. Cut the resistance wire at the points where it leaves the terminals, stretch it and find its length by the meter scale.
12. Record your observations.

Observations
1. Length

Length of the resistance wire  =....
2. Range

Range of the given ammeter =....
Range of the given voltmeter =....
3. Least count
Least count of ammeter =....
Least count of voltmeter =....
4. Zero error
Zero error in ammeter, e₁=....
Zero error in voltmeter, e₂=....
 Calculations
1. Find the ratio of V and I for each set of observations.
2. 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.

From the graph, the resistance can be calculated.

$
\begin{aligned}
& \text { in } \triangle A B C \quad \tan \theta=\frac{A B}{C B}=\frac{\Delta I}{\Delta V} \\
\Rightarrow & \cot \theta=\frac{\Delta V}{\Delta I} \\
\text { But } R & =\frac{\Delta V}{\Delta I}
\end{aligned}
$

So $R=\cot \theta$

$
R=\ldots \ldots \Omega
$

3. Constant ratio $\frac{V}{I}$ gives resistance of the wire.
4. Resistance of the wire per $\mathrm{cm}=\ldots$.

Result-
1. Resistance per cm of the wire is ......
2. The graph between V and I is a straight line.