Question

Two coils have self-inductance $L_1=4$$mH$ and $L_2=1$$mH$ respectively. The currents in the two coils are increased at the same rate. At a certain instant of time both coils are given the same power. If $i_1$ and $i_2$ are the currents in the two coils, at that instant of time respectively, then the value of ($i_1$ /$i_2$ ) is :

• A. $\frac{1}{8}$
• B. $\frac{1}{4}$
  
• C. $\frac{1}{2}$
• D. $1$

Answer 1

The correct option is B $\frac{1}{4}$

$V_1=L_1\frac{d{i}_1}{dt}$ $V_2=L_2\frac{d{i}_2}{dt}$

Power is same

$i_1{V}_1=V_2{i}_2$

$i_1{L}_1\frac{d{i}_1}{dt}=L_2\frac{d{i}_2}{dt}{i}_2$

$i_{1}4\times \frac{d{i}_1}{dt}=1.\frac{d{i}_2}{dt}{i}_2$

(same rate) current is increased from zero

$\therefore 4i_1=i_2$

$\frac{i_1}{i_2}=\frac{1}{4}$