Answer:
a) 0.83H
b) 3.22/N Henry
Explanation:
Given two inductors L1 = 1.31 H and L2 = 2.24 H connected in parallel, their equivalent inductance derivative is similar to that of resistance in parallel.
Derivation:
If the voltage across an inductor
VL = IXL
I is the current
XL is the inductive reactance
XL = 2πfL
VL = I(2πfL)
L is the inductance.
From the formula, I = V/2πfL
Given two inductors in parallel, different current will flow through them.
I1 = V/2πfL1 (current in L1)
I2 = V/2πfL2 (current in L2)
Total current I = I1+I2
I = V/2πfL1 + V/2πfL2
I = V/2πf{1/L1+1/L2}
V/2πfL = V/2πf{1/L1+1/L2}
1/L = 1/L1+1/L2 (equivalent inductance in parallel)
Given L1 = 1.31 H and L2 = 2.24
1/L = 1/1.31 + 1/2.24
1/L = 0.763 + 0.446
1/L = 1.209
L = 1/1.209
L = 0.83H
The equivalent inductance is 0.83H
b) Given similar inductors L = 3.22H in parallel, the equivalent inductance will be:
1/L = 1/3.22+1/3.22+1/3.22+1/3.22+1/3.22
+1/3.22+1/3.22+1/3.22+1/3.22+1/3.22
1/L = 10/3.22 (since that all have the same denominator)
L = 3.22/10
If N = 10, the generalization of 10 similar inductors in parallel will be:
L = 3.22/N Henry
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