Question

What resistance is needed in series with a 10-uF capacitor

at1.0kHz for a total impedance of 45 Ohm?

Answer 1

The value of resistance will be 42.08 ohm

Step-by-step explanation:

We have given capacitance
`C=10\mu F=10* 10^(-6)F`

Frequency f = 1 kHz = 1000 Hz

Impedance Z = 45 ohm

Capacitive reactance
`X_C=(1)/(\omega C)=(1)/(2\pi fC)=(1)/(2* 3.14* 1000* 10^(-5))=15.92ohm`

We know that impedance is given by
`Z=√(R^2+X_C^2)`

`45=√(R^2+15.92^2)`

Squaring both side
`2025=R^2+253.4464`

R = 42.08 ohm