Question

Determine the resistance per centimetre of the given wire by plotting a graph of potential difference vs current.

Hint:

To minimize errors, ensure all electrical connections are clean and tight. Take readings promptly after closing the key to prevent the wire from heating up, as an increase in temperature would change its resistance. Always check for and correct any zero error in the voltmeter and ammeter before starting.

Answer 1

Step 1: Understanding the Concept:
According to Ohm's Law, the potential difference (V) across the ends of a conductor is directly proportional to the current (I) flowing through it, provided the temperature and other physical conditions remain unchanged. Mathematically, V = IR, where R is the resistance. A graph of V versus I for an ohmic conductor is a straight line passing through the origin. The slope of this graph gives the resistance of the conductor. The resistance per unit length can then be found by dividing the total resistance by the length of the wire.
Step 2: Key Formula and Apparatus:
Apparatus Required:
A resistance wire, a battery eliminator, a DC voltmeter (0-5V), a DC ammeter (0-500mA), a rheostat, a plug key, a meter scale, and connecting wires.
Key Formula:
1. From Ohm's Law: \( R = \frac{V}{I} \)
2. From the graph, Resistance \( R = \text{Slope} = \frac{\Delta V}{\Delta I} \)
3. Resistance per centimetre \( r = \frac{R}{L} \), where L is the length of the wire in cm.
Step 3: Detailed Procedure:
1. Circuit Connection: Assemble the circuit by connecting the resistance wire, battery, ammeter, rheostat, and key in series. Connect the voltmeter in parallel across the resistance wire.
2. Data Collection: - Ensure the pointers of the ammeter and voltmeter are at their zero marks.
- Insert the key. Adjust the rheostat slider so that a small current flows through the circuit.
- Record the readings of the ammeter (I) and the voltmeter (V).
- Gradually move the slider of the rheostat to increase the current in steps and record the corresponding V and I readings for at least five different settings.
3. Measurement of Length: Measure the length (L) of the resistance wire used in the circuit using a meter scale.
Step 4: Graph and Calculation:
1. Plotting: Plot a graph with potential difference V along the Y-axis and current I along the X-axis, choosing a suitable scale. The graph should be a straight line passing through the origin.
2. Calculating Resistance (R): Find the slope of the V-I graph. The slope represents the resistance R of the wire. \[ R = \text{Slope} = \frac{BC}{AC} = \frac{\Delta V}{\Delta I} \, \Omega \] 3. Calculating Resistance per Centimetre (r): Calculate the resistance per centimetre using the measured length L. \[ r = \frac{R}{L} \, \Omega/\text{cm} \] The result is stated as the resistance per centimetre of the given wire.