LC resonance, Q factor & bandwidth worksheet with answers

Free printable LC resonance, Q factor & bandwidth worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A 470 nF capacitor is charged to 5 V and then connected to an ideal 22 mH inductor. Find the total energy W that swings between them, in µJ.

C = 470 nFV₀ = 5 VL = 22 mH

W = µJ

2.Easy

A 220 nF capacitor charged to 3 V is switched across an ideal 4.7 mH inductor. Find the peak current I_max in the circuit, in mA.

C = 220 nFV₀ = 3 VL = 4.7 mH

I_max = mA

3.Medium

A series RLC circuit resonates at 10 kHz with Q = 2. Find the lower half-power frequency f₁ exactly, in kHz.

f₀ = 10 kHzQ = 2

f₁ = kHz

4.Medium

A 470 nF capacitor charged to 5 V oscillates with an ideal 0.47 µH inductor. Find the energy W_L stored in the inductor at the moment the capacitor voltage is 2.5 V, in µJ.

C = 470 nFV₀ = 5 Vv_C = 2.5 V

W_L = µJ

5.Hard

A series RLC circuit (R = 5 Ω, L = 470 µH, C = 47 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy E_cycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 470 µHC = 47 nFI_m = 10 mA

E_cycle = nJ

6.Hard

A parallel tank circuit is made of a 220 pF capacitor and a 470 µH coil with a winding resistance of 1 Ω. At resonance it behaves like a resistor, its dynamic resistance R_D = L/(C·r). Find R_D in kΩ.

L = 470 µHC = 220 pFr = 1 Ω

R_D = kΩ

Answer key

1. W = 5.875 µJ
2. I_max = 20.53 mA
3. f₁ = 7.808 kHz
4. W_L = 4.406 µJ
5. E_cycle = 7.383 nJ
6. R_D = 2136 kΩ

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