Electric Circuits
If two identical capacitors are connected in parallel across a constant voltage source, how does their combined capacitance compare to that of a single capacitor?
The combined capacitance is equal to that of one capacitor.
The combined capacitance is double that of one capacitor.
The combined capacitance is four times that of one capacitor.
The combined capacitance is half that of one capacitor.
If a 5 μF capacitor is charged up to 10 V and then isolated, what is the energy stored in the capacitor?
500 μJ
0.25 mJ
50 μJ
2 mJ
In which scenario would the potential difference across the plates of an uncharged capacitor initially increase at the fastest rate?
When isolated from any external circuitry or power sources.
When connected in series with another fully charged capacitor.
When connected to a battery through a low-resistance wire.
When connected to a battery through a high-resistance wire.
What impact would doubling the separation distance between the plates of a capacitor have on its capacitance?
The capacitance would increase by a factor of four because the field strength decreases exponentially with distance.
The capacitance would double.
The capacitance would be halved.
The capacitance would remain the same.
What is the time constant for a discharging RC circuit if 60% of the initial charge remains on the capacitor after 2 milliseconds?
2.0 \times 10^{-3} s
4.8 \times 10^{-3} s
1.0 \times 10^{-3} s
7.2 \times 10^{-3} s
When four identical capacitors are reconfigured from parallel formation into series formation within an isolated system, the stored energy changes by what factor?
Increases twofold
Increases by factor four
Decreases by factor four
Stays same
Which term best describes materials that can store electrical energy within an electric field?
Conductors
Dielectrics
Semiconductors
Resistors

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If the potential difference across a 5 μF capacitor is increased from 10 V to 20 V, what happens to the charge it stores?
The charge remains the same.
The charge halves.
The charge doubles.
The charge quadruples.
How does using spherical symmetry help when calculating electric fields around a spherical conductor with uniform surface charge?
It allows us to treat all points equidistant from the center as identical, simplifying calculations via Gauss's law.
By focusing on radial distances only, we can apply Coulomb's law more effectively for non-uniform charge distributions.
It ensures that no electric field exists inside since it cancels out completely within a conductor.
Spherical symmetry nullifies any internal charges contributing to external fields beyond its radius.
How does connecting capacitors in series affect their equivalent capacitance?
The equivalent capacitance decreases.
The equivalent capacitance increases.
The equivalent capacitance stays the same.
Each capacitor's individual capacitance increases.