Question

\(I-V\) characteristic of a copper wire of length \(L\) and area of cross-section \(A\) is shown in figure. The slope of the curve becomes

• A. More if experiment is performed at higher temperature
• B. More if a wire of steel of same dimension is used
• C. Less if the area of the wire is increased
• D. Less if the length of the wire is increased

Answer 1

The Correct Option is D

The I-V characteristic curve of a wire follows Ohm's Law, where the current \(I\) is directly proportional to the voltage \(V\) and inversely proportional to the resistance \(R\). The resistance \(R\) of the wire is given by: \[ R = \rho \cdot \frac{L}{A} \] Where:
\(\rho\) is the resistivity of the material,
\(L\) is the length of the wire,
\(A\) is the cross-sectional area. The slope of the I-V characteristic curve is related to the resistance of the wire. Since resistance is directly proportional to the length of the wire, increasing the length \(L\) will increase the resistance. A higher resistance results in a lower slope of the I-V characteristic curve. 

Thus, if the length of the wire is increased, the slope of the curve decreases.

Answer 2

The I-V characteristic of a conductor follows Ohm's Law, which is given by: \[ V = IR \] where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance of the wire. The resistance \( R \) of a wire is given by the formula: \[ R = \rho \frac{L}{A} \] where:
\( \rho \) is the resistivity of the material,
\( L \) is the length of the wire,
\( A \) is the cross-sectional area of the wire. 

The slope of the I-V characteristic curve is given by \( \frac{1}{R} \).
Hence, the slope of the curve is: \[ \text{slope} = \frac{1}{R} = \frac{A}{\rho L} \] From this, we can observe the following: - If the length \( L \) of the wire increases, the slope of the curve (which is inversely proportional to \( L \)) decreases.
If the area \( A \) increases, the slope increases.
If the material's resistivity \( \rho \) increases (e.g., using a steel wire), the slope decreases. Thus, the slope of the I-V curve becomes less if the length of the wire is increased.

Therefore, the correct answer is \({D} \).