When does a capacitor become anti-battery resisting current as much as the battery drives it?

When does a capacitor become anti-battery resisting current as much as the battery drives it?

• A. When its voltage matches the battery's voltage
• B. When it is completely discharged
• C. When it is connected in parallel with a resistor
• D. When it is charged to double the battery's voltage

Answer: (D)

A capacitor resists changes in voltage, so in a DC setup it charges up to the source voltage and then no net current flows. If the capacitor’s voltage is higher than the battery’s, the capacitor will push charge back toward the source, creating a current in the opposite direction to the battery’s drive. The stronger the difference, the stronger that reverse current. When the capacitor is charged to double the battery’s voltage and then connected to the battery, charge flows from the capacitor back toward the battery to reduce the capacitor’s voltage toward the battery’s level. In that transient, the reverse current from the capacitor can oppose the battery’s forward current with comparable magnitude, which is what’s meant by the capacitor acting as an anti-battery—you get opposing currents that can largely cancel each other out in the external circuit. If the capacitor’s voltage already matches the battery’s, there’s no driving difference and thus no substantial opposing current. If the capacitor is completely discharged, the battery drives current into it rather than having it push current back. The parallel-with-a-resistor case doesn’t inherently create an opposing, canceling current by itself; it simply provides a path for current determined by the RC values.

A capacitor resists changes in voltage, so in a DC setup it charges up to the source voltage and then no net current flows. If the capacitor’s voltage is higher than the battery’s, the capacitor will push charge back toward the source, creating a current in the opposite direction to the battery’s drive. The stronger the difference, the stronger that reverse current.

When the capacitor is charged to double the battery’s voltage and then connected to the battery, charge flows from the capacitor back toward the battery to reduce the capacitor’s voltage toward the battery’s level. In that transient, the reverse current from the capacitor can oppose the battery’s forward current with comparable magnitude, which is what’s meant by the capacitor acting as an anti-battery—you get opposing currents that can largely cancel each other out in the external circuit.

If the capacitor’s voltage already matches the battery’s, there’s no driving difference and thus no substantial opposing current. If the capacitor is completely discharged, the battery drives current into it rather than having it push current back. The parallel-with-a-resistor case doesn’t inherently create an opposing, canceling current by itself; it simply provides a path for current determined by the RC values.