Question

What capacitor in series with a resistor $100\Omega$and a $20mH$inductor will give a resonance frequency of$1000Hz$

Short answer

Capacitor of $50\mu F$will give us resonance frequency of $1000Hz$

Step-by-step solution

Given Information

We are given that in series RLC circuit

$$\begin{gathered} R=100\Omega \\ L=20mH=20\times {10}^{-3}H \\ \omega =1000Hz \end{gathered}$$

Explanation

Let value of capacitance be $C$

As we know condition of resonance $i.e\omega =1/\sqrt{LC}$

putting value of capacitance ,inductance and resonance frequency in above equation we get,

$1000=1/\sqrt{C\times 20\times {10}^{-3}}$

Squaring both sides,

$$\begin{gathered} C=1/20000 \\ C=50\mu F \end{gathered}$$

Hence, capacitor of $50\mu F$will give us resonance frequency of $1000Hz$.