Question 3(c) Achieved

Kate builds a series circuit with a signal generator at 200 Hz, an AC ammeter, a lamp of 15.0 Ω and a 1.20 µF capacitor.

A 0.200 H inductor is added in series with the capacitor. At 2000 Hz the lamp is off; as the frequency is slowly reduced it suddenly glows brightly, then goes off again at lower frequencies.

Calculate the frequency at which the bulb glows brightest.

The 2023 paper, page 9 ↗ Marking schedule, page 6 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1. 1 When does the lamp glow brightest?

   When the current is largest, which is at resonance: X_L = X_C, so Z = R.

2. 2 Which formula gives the resonant frequency?

   f₀ = 1 / (2π√(LC)).

3. 3 Substitute, with C in farads.

   f₀ = 1 / (2π√(0.200 × 1.20 × 10⁻⁶)) = 1 / (2π × 4.899 × 10⁻⁴) = 325 Hz.

4. 4 Check it.

   At 325 Hz, X_L = 2π × 325 × 0.200 = 408 Ω and X_C = 1 / (2π × 325 × 1.20 × 10⁻⁶) = 408 Ω. Equal, as they should be.

What the marker wanted

• Achieved The resonant frequency, 325 Hz.

In our words, from NZQA’s 2023 marking schedule.

How did it go?

Got it moves it further out. Review brings it back tomorrow.