Grade 10 electricity – Capacitors and Capacitance Quiz
1. What is a capacitor?
A capacitor stores electric charge on two conducting plates separated by an insulating material (dielectric), allowing it to hold energy in an electric field.
2. What is the unit of capacitance?
Capacitance is measured in farads (F). One farad equals one coulomb of charge per volt (1 F = 1 C/V).
3. Which formula relates capacitance (C), charge (Q) and voltage (V)?
By definition, capacitance C equals the stored charge Q divided by the voltage V across the capacitor (C = Q/V).
4. For a parallel-plate capacitor, which change increases the capacitance?
Capacitance for parallel plates is proportional to plate area (C ∝ A). Larger area gives more capacitance. Increasing separation decreases C, and lower permittivity decreases C.
5. Which factor does NOT increase the capacitance of a parallel-plate capacitor?
Capacitance increases with dielectric constant (permittivity). Decreasing dielectric constant lowers capacitance, so it does not increase it.
6. What happens to a capacitor in a DC circuit after a long time when connected to a battery?
In steady-state DC, no current flows through an ideal capacitor once charged; it holds a voltage and acts like an open circuit.
7. How does a dielectric between capacitor plates affect capacitance?
A dielectric raises the permittivity between plates, reducing the field for a given charge so more charge can be stored at the same voltage, increasing capacitance.
8. What is the energy stored in a capacitor with capacitance C and voltage V?
The energy (in joules) stored in a capacitor is (1/2)CV^2, derived from integrating the work to charge the capacitor.
9. Two capacitors are connected in parallel. What is the total capacitance?
Parallel capacitors add directly because their plate areas effectively add, so C_total = C1 + C2 + ...
10. Two capacitors are connected in series. What is the correct expression for total capacitance Ctotal?
For series capacitors the reciprocals add (like resistors in parallel), so 1/Ctotal = 1/C1 + 1/C2, giving a smaller overall capacitance.
11. Which of these is a common use of capacitors in everyday electronics?
Capacitors smooth out fluctuations (ripples) in DC supplies by storing and releasing charge, stabilizing the output voltage.
12. What happens to the reactance of a capacitor when the frequency of the applied AC increases?
Capacitive reactance Xc = 1/(2πfC). As frequency f increases, Xc decreases, so the capacitor passes more AC current.
13. In an AC circuit, how does the current through a capacitor relate to the voltage across it?
In an ideal capacitor, AC current leads the voltage by 90° because current is proportional to the rate of change of voltage.
14. What is the formula for the capacitance of a parallel-plate capacitor with area A, plate separation d, and permittivity ε?
For parallel plates, capacitance C = εA/d, where ε is the permittivity of the dielectric between plates, A is plate area, and d is separation.
15. Which unit is most practical for everyday capacitors used in school experiments?
Everyday capacitors are commonly in microfarads (µF), or sometimes nanofarads (nF) or picofarads (pF); farads are usually too large.
16. If a 2 µF capacitor is charged to 10 V, what is the charge stored? (1 µF = 10^-6 F)
Charge Q = C × V = 2×10^-6 F × 10 V = 20×10^-6 C (or 2.0×10^-5 C).
17. What is dielectric breakdown in a capacitor?
Dielectric breakdown occurs if the electric field is too high, causing the dielectric to conduct and the capacitor to fail or short-circuit.
18. Why do real capacitors have a leakage current?
Real dielectrics have imperfections and finite resistance, causing a small leakage current that slowly discharges the capacitor.
19. What does the time constant τ (tau) in an RC circuit represent?
In an RC charging circuit, τ = R×C. After one τ, the capacitor charges to about 63% of the final voltage (or discharges to about 37%).
20. Which material property of the dielectric appears in the parallel-plate capacitance formula as ε = ε0 × εr?
ε = ε0εr, where ε0 is vacuum permittivity and εr is the relative permittivity (dielectric constant) of the material, affecting capacitance.
21. How can capacitors be used to block DC but pass AC in circuits?
A capacitor allows current when voltage changes (AC) because current depends on dV/dt; for steady DC it charges and then blocks further current.
22. What is meant by the term 'capacitance per unit area' for a parallel-plate capacitor?
Capacitance per unit area (C/A) indicates how much capacitance is produced by a given area and is equal to ε/d for parallel plates.
23. Which choice best describes a polarized capacitor (like an electrolytic capacitor)?
Polarized capacitors have an internal structure that requires correct polarity; reversing them can cause damage or explosion.
24. If you connect a large capacitor to a car battery, what safety precaution should you take?
Large capacitors can store hazardous charge. Always discharge through a resistor and avoid shorting terminals which can damage the capacitor or cause sparks.
25. Which statement about the behaviour of a capacitor at very high frequency is correct?
At very high frequencies capacitive reactance is very small, so the capacitor offers little opposition to AC and acts like a short for those frequencies.
26. What is the effect of connecting capacitors with the same capacitance in series on the total capacitance?
Series connection reduces total capacitance; for equal C values the total is C/n, so it's always less than the individual capacitances.
27. Which property of a capacitor determines how quickly it can charge and discharge in combination with a resistor?
The RC time constant τ = R×C determines charging/discharging speed: larger C or R gives slower response; colour or melting point are irrelevant.