Question

Aluminium$(\alpha =4\times {10}^{-3}{K}^{-1})$ resistance of 60$\Omega$ and carbon $(\alpha =0.5\times {10}^{-3}{K}^{-1})$ resistance 40$\Omega$ are connected in parallel. The combination is heated. The effective resistance is

• A. Greater than 24$\Omega$
• B. Less than 24$\Omega$
• C. Greater than 40$\Omega$
• D. Greater than 100$\Omega$

Answer 1

Answer: (B)

Less than 24$\Omega$

$R_{eff}=\frac{R_A{R}_C}{R_A+R_C}$

Before heating $=\frac{60\times 40}{100}=24\Omega$

$\frac{\Delta R_{eff}}{R_{eff}}=\frac{-\Delta R_A}{R_A}-\frac{\Delta R_B}{R_B}$

${\alpha }_{eff}\Delta T=\Delta T(-{\alpha }_A-{\alpha }_B)$

$\Rightarrow {\alpha }_{eff}=-({\alpha }_A+{\alpha }_B)$