Question

What happens to the voltage across the capacitor as it charges?

Option 1: The voltage across the capacitor remains constant.
Option 2: The voltage across the capacitor decreases.
Option 3: The voltage across the capacitor increases.
Option 4: The voltage across the capacitor fluctuates.
What occurs with the voltage across the resistor as the capacitor charges?

Option 1: The voltage across the resistor remains constant.
Option 2: The voltage across the resistor increases.
Option 3: The voltage across the resistor drops.
Option 4: The voltage across the resistor fluctuates.
How does the circuit current behave when a capacitor charges in the circuit?

Option 1: The circuit current remains constant.
Option 2: The circuit current increases continuously.
Option 3: The circuit current starts at its maximum possible value and then falls to zero.
Option 4: The circuit current fluctuates as the capacitor charges.

Answer 1

The voltage across a charging capacitor increases from initially zero to near the battery voltage asymptotically.

Step-by-step explanation:

As a capacitor charges, the voltage across the capacitor increases. When initially connected to a battery or power source, the voltage across the capacitor is zero and current flow is at its maximum. As the capacitor accumulates charge, the voltage increases according to the equation V = emf(1 - e-t/RC), where V is the voltage across the capacitor, emf is the electromotive force of the battery, R is the resistance in the circuit, t is time, and C is the capacitance. The voltage increase is not linear; it initially rises rapidly and then more slowly, approaching the emf, or maximum voltage of the battery, asymptotically.

Answer 2

The voltage across the capacitor increases as it charges, the voltage across the resistor decreases as the capacitor charges, and the circuit current starts at its maximum and falls to zero as the capacitor charges.

Step-by-step explanation:

When considering what happens to the voltage across the capacitor as it charges, we can refer to the formula derived using calculus: V = emf(1 - e-t/RC) for a charging capacitor. From this formula, we can conclude that the voltage across the capacitor increases as it charges. Option 3 is the correct choice for the behavior of the voltage across the capacitor.

As for the voltage across the resistor, this is linked to the current through the resistor (since V=IR), which decreases as the capacitor charges. Therefore, the voltage across the resistor decreases while the capacitor charges, making Option 3 correct for the behavior of voltage across the resistor.

Lastly, the circuit current behavior upon charging the capacitor can be understood by knowing that it starts at its maximum value and decreases as the capacitor charges up, eventually falling to zero. Thus, Option 3 correctly describes the circuit current behavior as the capacitor charges in the circuit.