Define resistance of a conductor. State the factors on which resistance of a conductor depends. Name the device which is often used to change the resistance without changing the voltage source in an electric circuit.
Calculate the resistance of $50 \, m$ length of wire of cross-sectional area $0.01 \, mm^2$ and of resistivity $5 \times 10^{-8} \, \Omega \, m$.

(D) Resistance is defined as the opposition offered by a conductor to the flow of electric current.
It depends on the following factors:
$(i)$ Nature of the material of the conductor.
$(ii)$ Length of the conductor $(L)$.
$(iii)$ Area of cross-section of the conductor $(A)$.
$A$ rheostat or variable resistor is the device used to change the resistance in an electric circuit without changing the voltage source.
Calculation:
Given: $L = 50 \, m$,$A = 0.01 \, mm^2 = 0.01 \times 10^{-6} \, m^2$,$\rho = 5 \times 10^{-8} \, \Omega \, m$.
Using the formula $R = \frac{\rho L}{A}$:
$R = \frac{5 \times 10^{-8} \times 50}{0.01 \times 10^{-6}}$
$R = \frac{250 \times 10^{-8}}{10^{-8}}$
$R = 250 \, \Omega$.