Discussion
If an air core solenoid with self-inductance of 0.5 mH is filled with soft iron of relative permeability of 1500, its self-inductance becomes
Answer: E
The self-inductance becomes 0.75 H.
A solenoid's self-inductance is \(L = \mu_r\mu_0 n^{2}Al\), so filling it with a core multiplies \(L\) by the relative permeability:
\[ \begin{aligned} L &= 1500 \times 0.5\ \text{mH} \\ &= 750\ \text{mH} = 0.75\ \text{H} \end{aligned} \]
0.5 H keeps the number 0.5 but switches the unit, which is not what the core does; 1.5 H and 1.25 H are not equal to 1500 times 0.5 mH.
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