The capacitor, reactance and impedance
Answers are for parents and teachers.
1
A capacitor of 15 µF is charged to 40 V. Find the charge. What voltage would a charge of 120 µC give on the same capacitor?
Q = 15 × 10⁻⁶ × 40 = 6.0 × 10⁻⁴ C = 600 µC. For 120 µC: V = Q ÷ C = 120 × 10⁻⁶ ÷ 15 × 10⁻⁶ = 8 V.
2
A capacitor of 20 µF is on a 60 V, 50 Hz supply (π = 3.14). Find XC and the effective current.
XC = 1 ÷ (2 × 3.14 × 50 × 20 × 10⁻⁶) = 1 ÷ 0.00628 = 159.2 Ω. I = 60 ÷ 159.2 = 0.38 A.
3
Capacitors of 6 µF and 12 µF are in series, and this pair is in parallel with a 5 µF capacitor. Find the total capacitance.
Series pair: (6 × 12) ÷ 18 = 4 µF. In parallel with 5 µF: 4 + 5 = 9 µF.
4
R = 15 Ω and XL = 20 Ω are in series on a 100 V supply. Find Z, I, VR, VL, tan θ and θ (3-4-5 triangle), and say whether the voltage leads or lags.
Z = √(15² + 20²) = 25 Ω. I = 100 ÷ 25 = 4 A. VR = 60 V and VL = 80 V (√(60² + 80²) = 100 V ✓). tan θ = 20 ÷ 15 = 4/3, so θ = 53°. The circuit has a coil, so the voltage leads the current.
5
Spot the error. In a series RL circuit a student measures VR = 21 V and VL = 28 V and says that the supply is 49 V. Find the mistake and give the correct supply voltage.
The voltages are 90° apart, so they must be added as vectors: V = √(21² + 28²) = √1225 = 35 V.