Chapter 21, Problem 55P

To determine

(a)

To calculate the reactance and rms current.

Answer to Problem 55P

Solution:

$I_{rms}=14.69\text{mA }$

Explanation of Solution

Given:

Inductance, $L=260\text{mA }$

RMS Voltage, $V_{rms}=240\text{V }$

Frequency, $f=10\text{kHz }$

Formula:

The relation between the inductive reactance and the inductanceis given by

$X_L=2\pi fL$

Where, f is the frequency in Hz and L is the inductance in H.

Calculation:

Substituting the values of f and L in the above relation, we get

$X_L=2\pi \times 10000\times 0.260=16.34\text{ k}\Omega$

To determine

(b)

To calculate the rms current.

Answer to Problem 55P

Solution:

$I_{rms}=14.69mA$

Explanation of Solution

Given:

Inductance, $L=260\text{mA }$

RMS Voltage, $V_{rms}=240\text{V }$

Frequency, $f=10\text{kHz }$

To find the rms current we use the relation

$I_{rms}=\frac{V_{rms}}{X_L}$

Calculation:

Substituting the values of X_L and rms voltage in the above relation, we get

$I_{rms}=\frac{240}{16.34\times {10}^3}=14.69\times {10}^{-3}\text{ A}$

The rms current is 14.69 mA.