# Phasor circuit problem: 1 resistor, 1 capacitor, 1 inductor, 1 Voltage source

1. Apr 3, 2007

### VinnyCee

1. The problem statement, all variables and given/known data

What value of $\omega$ will cause the forced response $v_0$ in the circuit below to be zero?

http://img248.imageshack.us/img248/1854/problem934ao5.jpg [Broken]

2. Relevant equations

Phasor eqs.

3. The attempt at a solution

$$i\,=\,\frac{50\,-\,V_1}{2\Omega}\,=\,\frac{V_1\,-\,V_2}{5\,j\,\Omega}\,=\,\frac{V_2}{20\,j\,\Omega}$$

If I substitute $V_1\,=\,0$, then I get:

$$25\,=\,-\frac{V_2}{5\,j\,\Omega}\,=\,\frac{V_2}{20\,j\,\Omega}$$

How do I use this to find $\omega$?

Last edited by a moderator: May 2, 2017
2. Apr 3, 2007

### SGT

If you want Vo to be zero, the impedance of the series connection of the capacitor with the inductor must be zero.
You got the impedance of the capacitor wrong.
$$Z_C = \frac{-j}{\omega C}$$
$$Z_L = j \omega L$$

3. Apr 3, 2007

### VinnyCee

http://img99.imageshack.us/img99/4333/problem934part2xc6.jpg [Broken]

$$Z\,=\,\frac{1}{5j\omega}\,+\,20j\omega$$

$$V_{OUT}\,=\,\frac{Z}{Z\,+\,2\Omega}$$

We want $V_{OUT}$ to be zero:

$$0\,=\,\frac{\frac{1}{5j\omega}\,+\,20j\omega}{\frac{1}{5j\omega}\,+\,20j\omega\,+\,2\Omega}\,V_{IN}$$

$$0\,=\,\frac{1}{5j\omega}\,+\,20j\omega}$$

$$-\frac{1}{5j\omega}\,=\,20j\omega$$

$$\omega\,=\,\frac{1}{10}$$

Is that right?

Last edited by a moderator: May 2, 2017
4. Apr 3, 2007

### SGT

Yes, the impedance is zero at the resonant frequency $$\omega_0 = \frac{1}{(LC)^\frac{1}{2}} = \frac{1}{10}$$

Last edited by a moderator: May 2, 2017