Question

1. Consider an A.C. source of frequency `(200/pi)` Hz applied across a coil. For each value of V − I in the tabulation, evaluate inductive reactance and self-inductance of the coil.
   

   S. No.	V (volt)	I (A)	Inductive reactance	Self-inductance
   1	3.0	0.5
   2	6.0	1.0
   3	9.0	1.5

2. If a D.C. source be connected to the same coil, what would be the value of inductive reactance?

Answer 1

1. Given: Frequency of the A.C. source (f) = `200/pi` Hz

Angular frequency (ω) = 2 π f = `2 pi (200/pi)` = 400 rad/s

We will use the following formulas:

Inductive reactance (X_L) = `V/I`

Self-inductance (L) = `X_L/(2 pi f) = X_L/omega`

For S. No. 1:

Inductive reactance (X_L) = `3.0/0.5` = 6 Ω

Self-inductance (L) = `6/400` = 0.015 H

For S. No. 2:

Inductive reactance (X_L) = `6.0/1.0` = 6 Ω

Self-inductance (L) = `6/400` = 0.015 H

For S. No. 3:

Inductive reactance (X_L) = `9.0/1.5` = 6 Ω

Self-inductance (L) = `6/400` = 0.015 H

S. No.	V (volt)	I (A)	Inductive reactance	Self-inductance
1	3.0	0.5	6.0 Ω	0.015 H
2	6.0	1.0	6.0 Ω	0.015 H
3	9.0	1.5	6.0 Ω	0.015 H

2. For a D.C. source, the frequency (f) is zero.

The inductive reactance is given by the formula X_L = 2 π f L

Since f = 0, the inductive reactance becomes:

X_L = 2 π (0) L = 0 Ω

This means that for a D.C. source, the inductive reactance of the coil is zero. Hence, the opposition to current is only due to the resistance of the coil.