Amperes Circuital Law

According to the problem, the inductive reactance at

50%20%5C%2C%20%5Cmathrm%7BHz%7D

is:

X_L%20%3D%2020%20%5C%2C%20%5COmega.

The inductive reactance

X_L

is given by:

X_L%20%3D%202%5Cpi%20f%20L.

Substitute

f%20%3D%2050%20%5C%2C%20%5Cmathrm%7BHz%7D

and

X_L%20%3D%2020%20%5C%2C%20%5COmega

2%5Cpi%20%5Ctimes%2050%20%5Ctimes%20L%20%3D%2020.

Simplify:

L%20%3D%20%5Cfrac%7B20%7D%7B2%5Cpi%20%5Ctimes%2050%7D%20%3D%20%5Cfrac%7B1%7D%7B5%5Cpi%7D%20%5C%2C%20%5Cmathrm%7BH%7D.

If the frequency is increased to

100%20%5C%2C%20%5Cmathrm%7BHz%7D

, the new inductive reactance is:

X_L%20%3D%202%5Cpi%20f%20L.

Substitute

f%20%3D%20100%20%5C%2C%20%5Cmathrm%7BHz%7D

and

L%20%3D%20%5Cfrac%7B1%7D%7B5%5Cpi%7D%20%5C%2C%20%5Cmathrm%7BH%7D

X_L%20%3D%202%5Cpi%20%5Ctimes%20100%20%5Ctimes%20%5Cfrac%7B1%7D%7B5%5Cpi%7D%20%3D%2040%20%5C%2C%20%5COmega.

The impedance

Z

of the circuit is given by:

Z%20%3D%20%5Csqrt%7BR%5E2%20%2B%20X_L%5E2%7D.

Substitute

R%20%3D%2030%20%5C%2C%20%5COmega

and

X_L%20%3D%2040%20%5C%2C%20%5COmega

Z%20%3D%20%5Csqrt%7B30%5E2%20%2B%2040%5E2%7D%20%3D%20%5Csqrt%7B900%20%2B%201600%7D%20%3D%20%5Csqrt%7B2500%7D.

Simplify:

Z%20%3D%2050%20%5C%2C%20%5COmega.

The current

I

is calculated using Ohm's Law:

I%20%3D%20%5Cfrac%7BV%7D%7BZ%7D.

Substitute

V%20%3D%20200%20%5C%2C%20%5Cmathrm%7BV%7D

and

Z%20%3D%2050%20%5C%2C%20%5COmega

I%20%3D%20%5Cfrac%7B200%7D%7B50%7D%20%3D%204%20%5C%2C%20%5Cmathrm%7BA%7D.

Thus, the current flowing through the coil is:

I%20%3D%204%20%5C%2C%20%5Cmathrm%7BA%7D.

Chapter Questions
2 MCQs