Question

An ac generator has a frequency of 7.7 kH.z and a voltage of 43 V. When an inductor is connected between the terminals of this generato1 the current in the inductor is 46 mA. What is the inductance of the inductor

Answer 1

The inductance of the inductor is 19.3 mH

Step-by-step explanation:

Inductance can be calculated from capacitive reactance,and it is given as;

`X_l = \omega L\\\\L = (X_l)/(\omega)\\\\L = (X_l)/(2\pi f)`

Apply ohms law to replace the capacitive reactance by voltage and current;

`L = (X_l)/(2\pi f)\\\\L = X_L((1)/(2\pi f) )\\\\L = (V)/(I) ((1)/(2\pi f))`

Substitute the given values;

`L = (V)/(I) ((1)/(2\pi f))\\\\L = (43)/(46*10^(-3)) ((1)/(2\pi (7.7*10^3)))\\\\L = 0.0193 \ H\\\\L = 19.3 \ mH`

Therefore, the inductance of the inductor is 19.3 mH