A capacitor has been connected to a 5V DC battery for a long time. Which statement correctly describes the current through the capacitor?
ACurrent flows steadily, proportional to the 5V and the capacitance
BCurrent is zero, because voltage is constant and i = C(dv/dt)
CCurrent flows in pulses as charge redistributes on the plates
DCurrent is zero only if the capacitor is fully charged; otherwise it flows continuously
The capacitor's defining relationship is i = C(dv/dt). In DC steady state the voltage is constant, so dv/dt = 0 and therefore current is zero — regardless of the voltage level. This is why capacitors block DC. The common misconception is treating capacitors like resistors, where current depends on voltage itself rather than on how fast voltage is changing.
Question 2 Multiple Choice
You suddenly interrupt the current through a large inductor that has been carrying 10A steadily. What happens that would NOT occur if you interrupted 10A through a resistor instead?
AThe inductor dissipates its stored energy as heat faster than the resistor would
BA large voltage spike appears across the inductor as it resists the sudden current change
CThe current drops to zero instantly, just as in the resistor
DNothing different — both elements respond identically to current interruption
An inductor's voltage is v = L(di/dt). Opening a switch changes current very rapidly (large di/dt), so the inductor produces a large voltage spike to oppose the change. This is why disconnecting an inductor abruptly can arc across a switch or destroy components. A resistor has no such behavior: once current stops, voltage immediately drops to zero because resistors have no stored energy to release.
Question 3 True / False
An ideal inductor carrying a constant 3A current has zero voltage across its terminals.
TTrue
FFalse
Answer: True
True. An inductor's voltage is v = L(di/dt). When current is constant, di/dt = 0, so v = 0. An ideal inductor looks like a short circuit under DC steady-state conditions. This is the dual of a capacitor in DC steady state: a capacitor is open (no current), while an inductor is short (no voltage).
Question 4 True / False
A capacitor and a resistor behave identically when connected to a constant DC voltage source — both allow a steady current proportional to the applied voltage.
TTrue
FFalse
Answer: False
False. A resistor passes a constant current proportional to voltage (I = V/R). A capacitor in DC steady state passes zero current, because its current depends on the rate of change of voltage, not the voltage itself. Resistors dissipate energy continuously; capacitors store it and block DC. A capacitor acts as an open circuit in DC steady state.
Question 5 Short Answer
Why do capacitors and inductors respond to the rate of change of a signal rather than to its instantaneous value, and what practical consequence does this have for DC circuits?
Think about your answer, then reveal below.
Model answer: Capacitors and inductors are defined by derivative relationships — i = C·dv/dt and v = L·di/dt — not by proportional ones. Their response depends on how fast voltage or current is changing. In DC circuits where nothing changes, both derivatives are zero, so capacitors pass no current (open circuit) and inductors drop no voltage (short circuit). This makes them inactive in DC steady state but frequency-sensitive in AC circuits.
The derivative relationship is what makes these elements 'reactive' — they react to changes, not to levels. This is also why they store energy rather than dissipate it: a resistor converts electrical energy to heat continuously, while capacitors and inductors hold energy in fields and release it when conditions change. This frequency-sensitive behavior makes them the building blocks of filters, oscillators, and timing circuits.