Question

Two inductance coils made of different metal wires are having the same inductance. But their time constants are in the ratio $1:2$ Then the ratio of their resistances is :

• A. $1:2$
• B. $1:\sqrt{2}$
• C. $\sqrt{2}:1$
• D. $2:1$

Answer 1

The correct option is D $2:1$

we know, time constant $\left(\tau \right)=\frac{inductance\left(L\right)}{resistance\left(R\right)}$
here $L_1=L_2,\frac{{\tau }_1}{{\tau }_2}=\frac{1}{2}$
so, $\frac{R_1}{R_2}=\frac{{\tau }_2}{{\tau }_1}=\frac{2}{1}$