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(C) The self-inductance of an air-cored coil is given by $L = \frac{\mu_0 N^2 A}{l} = 0.1 \ H$. When a soft iron core with relative permeability $\mu_

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$1 \ H$

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(C) The self-inductance of an air-cored coil is given by $L = \frac{\mu_0 N^2 A}{l} = 0.1 \ H$. When a soft iron core with relative permeability $\mu_r = 1000$ is introduced and the number of turns $N$ is changed to $N' = \frac{N}{10}$,the new self-inductance $L'$ is given by: $L' = \frac{\mu_0 \mu_r (N')^2 A}{l}$. Taking the ratio of the two inductances: $\frac{L'}{L} = \frac{\mu_r (N')^2}{N^2} = \mu_r \left(\frac{N/10}{N}ight)^2 = 1000 	imes \left(\frac{1}{10}ight)^2$. $\frac{L'}{L} = 1000 	imes \frac{1}{100} = 10$. Therefore,$L' = 10 	imes L = 10 	imes 0.1 \ H = 1 \ H$.

An air-cored coil has a self-inductance of $0.1 \ H$. $A$ soft iron core of relative permeability $1000$ is introduced,and the number of turns is reduced to $\frac{1}{10}$ of the original. The new value of self-inductance is:

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