An ac circuit contains a resistance of $1 \mathrm{k} \Omega$, a capacitor of $0.1 \mu \mathrm{~F}$ and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately:

Question

Accepted Answer

D. 1. Recall that in a series LCR circuit, **resonance** occurs when $X_L = X_C$, and the frequency at which this happens is given by the resonance frequency formula.
$$
f_0 = \frac{1}{2\pi\sqrt{LC}}
$$

2. **Substitute** the given values $L = 1	imes10^{-3}\,	ext{H}$ and $C = 0.1	imes10^{-6}\,	ext{F}$ into the formula.
$$
f_0 = \frac{1}{2\pi\sqrt{(1	imes10^{-3})(0.1	imes10^{-6})}}
$$

3. **Simplify** the product under the square root and evaluate.
$$
f_0 = \frac{1}{2\pi\sqrt{1	imes10^{-10}}} = \frac{1}{2\pi	imes10^{-5}} \approx 15.9\,	ext{kHz}
$$

Hence, the resonance frequency is approximately **15.9 kHz**, so the correct answer is **option D**.

An ac circuit contains a resistance of 1kΩ1 \mathrm{k} \Omega1kΩ, a capacitor of 0.1μ F0.1 \mu \mathrm{~F}0.1μ F and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately:

An ac circuit contains a resistance of $1 \mathrm{k} \Omega$ , a capacitor of $0.1 \mu \mathrm{~F}$ and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately: