Answer :
Answer with Explanation:
We are given that
Inner radius of wooden toroidal core=[tex]r_1=14[/tex]cm
Outer radius of wooden toroidal core=[tex]r_2=16[/tex] cm
Diameter of wire=1.0 mm
Resistance per meter=0.020 ohm/m
a.We have to find the inductance of the toroid.
Inner circumference of toroid=[tex]2\pi r_1=2\times \frac{22}{7}\times 14=88[/tex] cm=880 mm
[tex]\pi=\frac{22}{7}[/tex]
1 cm=10 mm
Number of turns is roughly ,N=[tex]\frac{880}{1}\approx 880[/tex]
h=[tex]r_2-r_1=16-14=2 cm=0.02 m[/tex]
1 m=100 cm
Inductance of the toroid=[tex]\frac{\mu_0N^2h}{2\pi}ln\frac{r_2}{r_1}[/tex]
Substitute the values then, we get
[tex]L=\frac{4\pi\times 10^{-7}\times (880)^2\times 0.02}{2\pi}\times ln\frac{16}{14}[/tex]
[tex]\mu_0=4\pi\times 10^{-7}[/tex]
[tex]L=4.1\times 10^{-4} H[/tex]
Hence, the inductance of the toroid=[tex]4.1\times 10^{-7}[/tex] H
b.We have to find the inductive time constant of toroid.
Total length of wire=[tex]4(880)\times \frac{2}{100}=70.4 m[/tex]
Because, total number of turns=880
Perimeter of square = 4 times the side of the square
Side of square shaped loop=2 cm
Resistance of wire=[tex]70.4\times 0.02=1.408[/tex] ohm
Inductive time constant [tex]=\frac{L}{R}[/tex]
Inductive time constant=[tex]\frac{4.1\times 10^{-4}}{1.408}=2.91\times 10^{-4} s[/tex]
Hence, the inductive time constant of toroid=[tex]2.91\times 10^{-4} s[/tex]