Two wires of resistance R_1 and R_2 have temperature coefficient of resistance {alpha _1,}{rm{ and ,}}{alpha _2}, respectively. These are joined in series. The effective

Q: Two wires of resistance $R_1$ and $R_2$ have temperature coefficient of resistance ${\alpha _1\,}{\rm{ and \,}}{\alpha _2}$, respectively. These are joined in series. The effective temperature coefficient of resistance is

c (c) ${R_{{t_1}}} = {R_1}(1 + {\alpha _1}t)$ and ${R_{{t_2}}} = {R_2}(1 + {\alpha _2}t)$ Also ${R_{eq.}} = {R_{{t_1}}} + {R_{{t_2}}} \Rightarrow {R_{eq}} = {R_1} + {R_2}$$ + ({R_1}{\alpha _1} + {R_2}{\alpha _2})t$ $==>$ ${R_{eq}} = ({R_1} + {R_2})\left\{ {1 + \left( {\frac{{{R_1}{\alpha _1} + {R_2}{\alpha _2}}}{{{R_1} + {R_2}}}} \right).t} \right\}$ So ${\alpha _{eff}} = \frac{{{R_1}{\alpha _1} + {R_2}{\alpha _2}}}{{{R_1} + {R_2}}}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

Two wires of resistance $R_1$ and $R_2$ have temperature coefficient of resistance ${\alpha _1\,}{\rm{ and \,}}{\alpha _2}$, respectively. These are joined in series. The effective temperature coefficient of resistance is

A$\frac{{{\alpha _1} + {\alpha _2}}}{2}$
B$\sqrt {{\alpha _1}{\alpha _2}} $
C$\frac{{{\alpha _1}{R_1} + {\alpha _2}{R_2}}}{{{R_1} + {R_2}}}$
D$\frac{{\sqrt {{R_1}{R_2}{\alpha _1}{\alpha _2}} }}{{\sqrt {R_1^2 + R_2^2} }}$

Diffcult

STD 11 Science
NEET
STD 12 - 3. current electricity
Physics

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