Chapter 10, Problem 1TFQ

In a series RC circuit, the impedance increases when frequency increases.

To determine

The effect on the impedance of the given circuit due to increase in frequency.

Answer to Problem 1TFQ

The impedance does not increase when the frequency is increases for a series RC circuit.

Explanation of Solution

Given:

For series RC circuit, due to increase in frequency the impedance of the circuit also increases.

Drawing the general circuit diagram for the series RC circuit:

  

Referring the above circuit diagram, when the frequency is increased there is no change on the resistor value, because resistor do not depend upon the frequency of the system.

But for the capacitor, when the frequency of the system is increased, the capacitive reactance will decrease, because capacitive reactance is inversely proportional to the frequency.

  $\begin{array}{l}{X}_C=\frac{1}{j2\pi fC}\\ f\uparrow \alpha \frac{1}{X_C\downarrow }\end{array}$

Now, if the capacitive reactance is decreasing then in series connection, their resultant will also decrease.

As shown below, arrow is indicating frequency is increasing due to which overall impedance of the circuit decreases.

  $Z\downarrow =R+\left(\frac{1}{j2\pi f\uparrow C}\right)$

Therefore, the impedance does not increase when the frequency is increases for a series RC circuit.