Chapter 21, Problem 52P

To determine

(a) To determine:

To find the capacitive reactance at frequencies of $60\text{ Hz}$ and $1.00\text{ MHz}.$

Answer to Problem 52P

Solution:

The capacitive reactance is found to be $427.84\Omega$

Explanation of Solution

Given:

Capacitance, $C=6.2\mu F$

Frequency, $f=60\text{Hz to }1.0\text{MHz}$

Formula:

The relation between the capacitive reactance and the capacitance is given by

$X_C=\frac{1}{2\pi fC}$

Where, $f$ is the frequency in $\text{Hz}$ and $\text{C}$ is the capacitance in $\text{F}\text{.}$

Substituting the values of $f$ and $\text{C}$ in the above relation, we get

Calculation:

$X_C=\frac{1}{2\pi \times 60\times 6.2\times {10}^{-6}}=427.84\Omega$

The capacitive reactance at 60 Hz is $427.84\Omega$

To determine

(b) To determine:

To find the capacitive reactance at frequencies of $60\text{ Hz}$ and $1.00\text{ MHz}.$

Answer to Problem 52P

Solution:

The capacitive reactance is found to be $0.0257\Omega$

Explanation of Solution

Given:

Capacitance, $C=6.2\mu F$

Frequency, $f=60\text{Hz to }1.0\text{MHz}$

Calculation:

Similarly, we determine for the frequency of 1.0 MHz

$X_C=\frac{1}{2\pi \times 1\times {10}^6\times 6.2\times {10}^{-6}}=0.0257\Omega$

The capacitive reactance at 1.00 MHz is $0.0257\Omega$