Question

Two coils have self-inductances $L_1=8mH$ and $L_2=4mH$. The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the current, the induced voltage and the energy stored in the first coil are $i_1,V_1$ and $W_1$. Corresponding values for the second coil are $i_2,V_2$ and $W_2$ respectively. Then:
(IIT-JEE 1994)

• A. $\frac{i_1}{i_2}=4$
• B. $\frac{V_1}{V_2}=\frac{1}{4}$
• C. $\frac{W_1}{W_2}=\frac{1}{2}$
• D. $\frac{i_1}{i_2}=\frac{1}{4}$

Answer 1

The correct option is C $\frac{W_1}{W_2}=\frac{1}{2}$

and $\frac{d{i}_1}{dt}=\frac{d{i}_2}{dt}$ --- (1)
Also given, $\frac{V_1}{i_1}=\frac{V_2}{i_2}$
So since $V_1=L_1\frac{d{i}_1}{dt}$ and $V_2=L_2\frac{d{i}_2}{dt}$
We know, $\frac{V_1}{V_2}=\frac{L_1}{L_2}$ = $\frac{i_2}{i_1}=2$

This doesn't match 3 of the options so the fourth one has to be right. Let's solve it anyway.
$\frac{W_1}{W_2}=\frac{0.5L_1{i_1}^2}{0.5L_2{i_2}^2}=\frac{1}{2}$