Resistivity — Prelims Strategy

Prelims Strategy

To tackle NEET questions on resistivity effectively, adopt a multi-pronged strategy:

1
Master the Formulas: — Be thoroughly familiar with $R = \rho \frac{L}{A}$ and its rearrangement $\rho = \frac{RA}{L}$. Also, understand the microscopic formula $\rho = \frac{m}{ne^2\tau}$ for conceptual clarity. For temperature dependence, know $\rho_T = \rho_0 [1 + \alpha (T - T_0)]$.
2
Units and Conversions: — Always pay attention to units. Resistivity is in $\Omega \cdot \text{m}$. Ensure all lengths are in meters and areas in square meters. Be careful with $\text{mm}^2$ to $\text{m}^2$ conversions ($1\,\text{mm}^2 = 10^{-6}\,\text{m}^2$).
3
Dimensional Changes (Stretching/Compressing): — This is a high-yield area. Remember that when a wire is stretched or compressed, its volume ($V = AL$) remains constant. If length changes by a factor $x$, area changes by $1/x$. Consequently, resistance changes by $x^2$. For example, if length doubles, resistance becomes $4R$. Resistivity, however, remains constant.
4
Temperature Effects: — Clearly distinguish between conductors (resistivity increases with T) and semiconductors (resistivity decreases with T). Understand the underlying reasons (change in $\tau$ vs. change in $n$). Alloys have low $\alpha$.
5
Conceptual Clarity: — Do not confuse resistivity with resistance. Resistivity is a material property; resistance is an object property. Practice identifying which factors affect which.
6
Practice MCQs: — Solve a wide variety of MCQs, especially those involving dimensional changes and temperature dependence. Pay attention to trap options that confuse resistance with resistivity or misinterpret temperature effects.