Learning Goal: To understand the relationship between AC voltage and current in

Question

Learning Goal:

To understand the relationship between AC voltage and current in resistors, inductors, and capacitors, especially the phase shift between the voltage and the current.

In this problem, we consider the behavior of resistors, inductors, and capacitors driven individually by a sinusoidally alternating voltage source, for which the voltage is given as a function of time by V(t)=V0cos(t). The main challenge is to apply your knowledge of the basic properties of resistors, inductors, and capacitors to these "single-element" AC circuits to find the current I(t) through each. The key is to understand the phase difference, also known as the phase angle, between the voltage and the current. It is important to take into account the sign of the current, which will be called positive when it flows clockwise from the b terminal (which has positive voltage relative to the a terminal) to the a terminal (see figure). The sign is critical in the analysis of circuits containing combinations of resistors, capacitors, and inductors.

(Figure 1)

Part D

Consider the potentials of points a and b on the inductor in diagram 2. If the potential at point b is greater than that at point a, which of the following statements is true?

The derivative of the current dI(t)dtmust be positive.

Part G

Consider the capacitor in diagram 3. Which of the following statements is true at the moment the alternating voltage across the capacitor is zero?

Part H

Consider the capacitor in diagram 3. Which of the following statements is true at the moment the charge of the capacitor is at a maximum?

Part I

Consider the capacitor in diagram 3. Which of the following statements is true if the potential at point b is greater than the potential at point a?

Part J

Consider a circuit in which a capacitor and an inductor are connected in parallel to an AC source. Which of the following statements about the magnitude of the current through the voltage source is true?

At very low frequencies it will become small.

The current I(t) must be positive (clockwise). The current I(t) must be directed counterclockwise. The derivative of the current dI(t)dtmust be negative.

The derivative of the current dI(t)dtmust be positive.

Part G

Consider the capacitor in diagram 3. Which of the following statements is true at the moment the alternating voltage across the capacitor is zero?

The current must be directed clockwise. The current must be directed counterclockwise. The magnitude of the current must be a maximum. The current must be zero. I(t) I(t) I(t)

Explanation / Answer

Part(D) The derivative of the current dI(t)dtmust be positive.

Part(G) The magnitude of the current must be a maximum

Part(H) The current must be zero.

Part (I) The current may be directed either clockwise or counterclockwise

Part(J) It is always less than the sum of the magnitudes of the currents in the capacitor and inductor.

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