Capacitors In Circuits Quiz for Circuit Analysis Skills

1. In series, the equivalent capacitance ceq satisfies:

Ceq=c1+c2

1/ceq=1/c1+1/c2

Ceq=c1c2

Ceq=c1-c2

Concept: series capacitors rule. Series capacitors share the same charge, and voltages add. This leads to the reciprocal addition rule, making ceq smaller than either capacitor.

Explanation

Concept: series capacitors rule. Series capacitors share the same charge, and voltages add. This leads to the reciprocal addition rule, making ceq smaller than either capacitor.

2. The equivalent capacitance of capacitors in series is always less than the smallest individual capacitance.

True

False

Concept: series reduces capacitance. Series connection increases effective separation of charge storage, reducing total charge stored per volt.

Explanation

Concept: series reduces capacitance. Series connection increases effective separation of charge storage, reducing total charge stored per volt.

3. In parallel, the equivalent capacitance is:

1/ceq=1/c1+1/c2

Ceq=c1+c2

Ceq=c1-c2

Ceq=c1c2

Concept: parallel capacitors rule. Parallel capacitors share the same voltage, and charges add, making capacitances add directly.

Explanation

Concept: parallel capacitors rule. Parallel capacitors share the same voltage, and charges add, making capacitances add directly.

4. Two capacitors (c_1) and (c_2) in parallel store charge as if they were one bigger capacitor with (c_{eq} = ______).

Concept: parallel increases charge capacity. Since (q=cv), adding capacitance increases total charge stored for the same voltage.

Explanation

Concept: parallel increases charge capacity. Since (q=cv), adding capacitance increases total charge stored for the same voltage.

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5. In an RC circuit, the time constant is (tau = rc).

True

False

Concept: RC time constant. (\tau) sets the timescale for charging and discharging. Larger (r) or (c) makes the process slower.

Explanation

Concept: RC time constant. (\tau) sets the timescale for charging and discharging. Larger (r) or (c) makes the process slower.

6. If (r) is increased (same (c)), the capacitor charges:

Faster

More slowly

At the same rate

Instantly

Concept: resistance controls current. Higher resistance limits current flow, slowing the rate of charge transfer, which increases the time constant.

Explanation

Concept: resistance controls current. Higher resistance limits current flow, slowing the rate of charge transfer, which increases the time constant.

7. After one time constant (\tau), the charging capacitor voltage has reached about:

10% of final value

37% of final value

63% of final value

100% of final value

Concept: exponential charging landmark. Charging follows v(t)=v0(1-e^{-t/rc}). At t=τ, 1-e^{-1}≈0.63.

Explanation

Concept: exponential charging landmark. Charging follows v(t)=v0(1-e^{-t/rc}). At t=τ, 1-e^{-1}≈0.63.

8. During discharging, after one time constant the voltage falls to about 37% of its initial value.

True

False

Concept: exponential decay landmark. Discharge follows v(t)=v0e^{-t/rc}. At t=τ, e^{-1}≈0.37.

Explanation

Concept: exponential decay landmark. Discharge follows v(t)=v0e^{-t/rc}. At t=τ, e^{-1}≈0.37.

9. The energy stored in a capacitor is e=1/2 cv^2, measured in______.

Concept: energy in a capacitor. Energy comes from the work done to move charge onto the plates. The (v^2) shows that doubling voltage increases stored energy significantly.

Explanation

Concept: energy in a capacitor. Energy comes from the work done to move charge onto the plates. The (v^2) shows that doubling voltage increases stored energy significantly.

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10. A (2.0,\text{mf}) capacitor at 10 v stores energy:

0.01 j

0.10 j

1.0 j

10 j

Concept: using e=1/2 cv^2. c=0.002f, so e=0.5×0.002×100=0.1j. The unit is joules.

Explanation

Concept: using e=1/2 cv^2. c=0.002f, so e=0.5×0.002×100=0.1j. The unit is joules.

11. For a fixed capacitor, energy stored increases with the square of voltage.

True

False

Concept: v^2 dependence. From e=1/2 cv^2, doubling v multiplies energy by 4. This is why voltage ratings matter strongly.

Explanation

Concept: v^2 dependence. From e=1/2 cv^2, doubling v multiplies energy by 4. This is why voltage ratings matter strongly.

12. In a series pair of capacitors, the charge on each capacitor is:

Different because voltages differ

The same

Always zero

Random

Concept: series capacitors share charge. The same charge must flow through the series chain to charge each capacitor.

Explanation

Concept: series capacitors share charge. The same charge must flow through the series chain to charge each capacitor.

13. In a parallel pair of capacitors, the voltage across each capacitor is the same.

True

False

Concept: parallel shares voltage. Both capacitors connect to the same two nodes, forcing the same potential difference across each.

Explanation

Concept: parallel shares voltage. Both capacitors connect to the same two nodes, forcing the same potential difference across each.

14. In charging, current is initially ______ and then decreases toward zero (for a simple RC circuit).

Concept: charging current behavior. At (t=0), the capacitor has 0 v so the resistor sees the full supply voltage, giving maximum current.

Explanation

Concept: charging current behavior. At (t=0), the capacitor has 0 v so the resistor sees the full supply voltage, giving maximum current.

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15. In a graph of capacitor voltage vs time during charging, the shape is:

A straight line up

A curve that rises quickly then levels off

A curve that drops quickly then levels off

A constant line

Concept: exponential approach. Exponential charging rises rapidly at first, then slows as it approaches the final voltage.

Explanation

Concept: exponential approach. Exponential charging rises rapidly at first, then slows as it approaches the final voltage.

16. A capacitor acts like an open circuit for steady DC but like a low impedance path for rapidly changing signals (qualitatively).

True

False

Concept: frequency-dependent behavior. DC steady state means no ongoing current through the capacitor. Rapid changes require charge movement, allowing current to flow.

Explanation

Concept: frequency-dependent behavior. DC steady state means no ongoing current through the capacitor. Rapid changes require charge movement, allowing current to flow.

17. If you connect two identical capacitors in parallel, the total capacitance becomes:

Half of one capacitor

Twice one capacitor

The same as one capacitor

Four times one capacitor

Concept: parallel addition. Parallel capacitances add: ceq=c+c=2c, increasing charge storage at the same voltage.

Explanation

Concept: parallel addition. Parallel capacitances add: ceq=c+c=2c, increasing charge storage at the same voltage.

18. Increasing capacitance (same resistor) increases the time constant and makes charging slower.

True

False

Concept: (tau=rc) effect. Larger (c) means more charge must move to reach a given voltage, taking longer with the same resistance limiting current.

Explanation

Concept: (tau=rc) effect. Larger (c) means more charge must move to reach a given voltage, taking longer with the same resistance limiting current.

19. The charge stored on a capacitor can also be written (q=cv). For a given (c), increasing (v) increases (q) ______.

Concept: linear (q-v) relationship. Charge is proportional to voltage for an ideal capacitor, defining constant capacitance.

Explanation

Concept: linear (q-v) relationship. Charge is proportional to voltage for an ideal capacitor, defining constant capacitance.

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20. The best overall summary is:

Capacitors in series add directly

Parallel capacitors add; series capacitors add as reciprocals; RC circuits charge/discharge exponentially with τ=rc, and stored energy is 1/2 cv^2

Energy stored is (cv)

Time constant is (r/c)

Concept: connection rules determine equivalent capacitance. RC behavior is exponential and energy storage depends strongly on voltage.

Explanation

Concept: connection rules determine equivalent capacitance. RC behavior is exponential and energy storage depends strongly on voltage.

Capacitors In Circuits Quiz: Test Your Circuit Analysis Skills

1. In series, the equivalent capacitance ceq satisfies:

2.

What first name or nickname would you like us to use?

2. The equivalent capacitance of capacitors in series is always less than the smallest individual capacitance.

3. In parallel, the equivalent capacitance is:

4. Two capacitors (c_1) and (c_2) in parallel store charge as if they were one bigger capacitor with (c_{eq} = ______).

5. In an RC circuit, the time constant is (tau = rc).

6. If (r) is increased (same (c)), the capacitor charges:

7. After one time constant (\tau), the charging capacitor voltage has reached about:

8. During discharging, after one time constant the voltage falls to about 37% of its initial value.

9. The energy stored in a capacitor is e=1/2 cv^2, measured in______.

10. A (2.0,\text{mf}) capacitor at 10 v stores energy:

11. For a fixed capacitor, energy stored increases with the square of voltage.

12. In a series pair of capacitors, the charge on each capacitor is:

13. In a parallel pair of capacitors, the voltage across each capacitor is the same.

14. In charging, current is initially ______ and then decreases toward zero (for a simple RC circuit).

15. In a graph of capacitor voltage vs time during charging, the shape is:

16. A capacitor acts like an open circuit for steady DC but like a low impedance path for rapidly changing signals (qualitatively).

17. If you connect two identical capacitors in parallel, the total capacitance becomes:

18. Increasing capacitance (same resistor) increases the time constant and makes charging slower.

19. The charge stored on a capacitor can also be written (q=cv). For a given (c), increasing (v) increases (q) ______.

20. The best overall summary is: