Question

the impedance of rc circuit is z1 for frequency f and z2 for frequency 2f .then z1/z2 =?​

Answer 1

z1/z2 = 2

Given:

Frequency when impendence is z1 = f

Frequency when impendence is z2 = 2f

To find:

z1/z2 = ?

Formula used:

$\bold{z = \frac{1}{\omega C}}$

Where,

$\bold{\omega}$ is Angular Frequency

C is Capacitance

$\bold{\omega = 2 \pi f}$

Solution:

Impendence z1 is:

$\bold{z1 = \frac{1}{\omega_1 C}}$

$\bold{\omega_1 = 2 \pi f}$

$\bold{\therefore z1 = \frac{1}{2 \pi f C}}$

Impendence z2 is:

$\bold{z2 = \frac{1}{\omega_2 C}}$

$\bold{\omega_2 = 2 \pi 2f}$

$\bold{z2 = \frac{1}{2 \pi 2f C}}$

Now,

$\bold{\frac{z1}{z2}=\frac{\frac{1}{2 \pi f C}}{\frac{1}{2 \pi 2f C}}}$

$\bold{\frac{z1}{z2}=\frac{1}{2\pi fC}\times\frac{2 \pi 2f C}{1}}$

$\bold{\frac{z1}{z2}=\frac{2 \pi 2f C }{2 \pi f C }}$

$\bold{\therefore \frac{z1}{z2}=2}$