Question

g determine what frequency is required of a source powering a 100 uf capacitor a 500 ohm resistor and a s50 mH inductor in series do the current is maximized

Answer 1

Answer:
`71.16\ Hz`

Step-by-step explanation:

Given

Capacitance
`C=100\ \mu F`

Resistance
`R=500\ \Omega`

Inductance
`L=50\ mH`

In LCR circuit, current is maximum at resonance frequency i.e.

`X_L=X_C\ \text{and}\ \omega_o=(1)/(√(LC))`

Insert the values

`\Rightarrow \omega_o=\frac{1}{\sqrt{50* 10^(-3)* 100* 10^(-6)}}\\\\\Rightarrow \omega_o=(1)/(√(5)* 10^(-3))\\\\\Rightarrow \omega_o=0.447* 10^(3)`

Also, frequency is given by

`\Rightarrow 2\pi f=\omega_o\\\\\Rightarrow f=(\omega_o)/(2\pi)`

`\Rightarrow f=(1)/(2\pi)* 0.447* 10^3\\\\\Rightarrow f=71.16\ Hz`