Back to Exercise: Capacitors and Dielectrics

Exercises: Capacitors and Dielectrics

Work through each section in order. Show your work for all calculation problems. Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2/(\text{N·m}^2)$ where needed.

Grade 11·21 problems·~30 min·OpenStax Physics (High School)·section·sec-18-5

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Recall / Warm-Up

Which best describes what a capacitor does in a circuit?

It stores separated electric charge and maintains a potential difference between two conductors.

It converts electrical energy to chemical energy for long-term storage.

It stores electric current and releases it when the circuit opens.

It resists changes in current, similar to an inductor.

A parallel-plate capacitor is connected to a 12 V battery. The voltage across the capacitor is:

12 V, equal to the battery voltage.

Less than 12 V, because the capacitor uses up some voltage.

More than 12 V, because the capacitor amplifies voltage.

Zero, because the capacitor blocks DC.

When a dielectric material is inserted between the plates of a charged capacitor (with the plates disconnected from any battery), what happens to the voltage across the plates?

The voltage decreases because the dielectric reduces the electric field.

The voltage increases because the dielectric increases the capacitance.

The voltage stays the same because charge is conserved.

The voltage increases because the dielectric strengthens the field.

Fluency Practice

A capacitor stores $Q = 180\ \mu\text{C}$ of charge when connected to a $V = 9\ \text{V}$ source. What is the capacitance in microfarads?

A $47\ \mu\text{F}$ capacitor is connected to a $5.0\ \text{V}$ source. How much charge is stored on the capacitor, in microcoulombs?

A capacitor with $C = 100\ \mu\text{F}$ stores $Q = 500\ \mu\text{C}$ of charge. A second capacitor with $C = 500\ \mu\text{F}$ stores the same charge $Q = 500\ \mu\text{C}$ . Which capacitor has the higher voltage across its plates?

The $100\ \mu\text{F}$ capacitor — it has a voltage of 5 V, five times higher than the $500\ \mu\text{F}$ capacitor.

The $500\ \mu\text{F}$ capacitor — larger capacitance means larger voltage for the same charge.

Both have the same voltage — they store the same charge.

Cannot be determined without knowing the plate area.

A $200\ \mu\text{F}$ capacitor is charged to $V = 300\ \text{V}$ . Calculate the energy stored in the capacitor in joules.

A capacitor stores $U = 0.050\ \text{J}$ of energy at a voltage of $V = 100\ \text{V}$ . What is the capacitance in microfarads?

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