Question

Two inductors each of inductance L are connected in parallel. One more inductor of value $5$ mH is connected in series of this configuration then the effective inductance is $15$ mH. The value of L is ___________ mH.

• A. $10$
• B. $5.0$
• C. $2.5$
• D. $20$

Answer 1

The correct option is D $20$

Equivalent inductance in parallel connection $\frac{1}{L_p}=\frac{1}{L_1}+\frac{1}{L_2}$
$\therefore$ $\frac{1}{L_p}=\frac{1}{L}+\frac{1}{L}=\frac{2}{L}$
We get $L_p=\frac{L}{2}$
This combination is connected in series with $L_3=5mH$.
Equivalent inductance $L_{eq}=L_p+L_3$
$\therefore$ $15=\frac{L}{2}+5$
$⟹L=20mH$
So, correct answer is option D.