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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) = V0 cos(?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. Part A First, let us consider a resistor with resistance R connected to an AC source (diagram 1). If the AC source provides a voltage VR(t) = V0 cos(?t), what is the current IR(t) through the resistor as a function of time? Express your answer in terms of V0, R, ?, and t. IR(t) = Part B Now consider an inductor with inductance L in an AC circuit (diagram 2). Assuming that the current in the inductor varies as IL(t) = I0 cos(?t), find the voltage VL(t) that must be driving the inductor. Express your answer in terms of I0, L, ?, and t. Use the cosine function, not the sine function, in your answer. VL(t) = Part C Again consider an inductor with inductance L connected to an AC source. If the AC source provides a voltage VL(t) = V0 cos(?t), what is the current IL(t) through the inductor as a function of time? Express your answer in terms of V0, L, ?, and t. Use the cosine function, not the sine function, in your answer. IL(t) =

          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) = V0 cos(?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.

Part A
First, let us consider a resistor with resistance R connected to an AC source (diagram 1). If the AC source provides a voltage VR(t) = V0 cos(?t), what is the current IR(t) through the resistor as a function of time?
Express your answer in terms of V0, R, ?, and t.
IR(t) =

Part B
Now consider an inductor with inductance L in an AC circuit (diagram 2). Assuming that the current in the inductor varies as IL(t) = I0 cos(?t), find the voltage VL(t) that must be driving the inductor.
Express your answer in terms of I0, L, ?, and t. Use the cosine function, not the sine function, in your answer.
VL(t) =

Part C
Again consider an inductor with inductance L connected to an AC source. If the AC source provides a voltage VL(t) = V0 cos(?t), what is the current IL(t) through the inductor as a function of time?
Express your answer in terms of V0, L, ?, and t. Use the cosine function, not the sine function, in your answer.
IL(t) =

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) = V0 cos(?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.

Part A
First, let us consider a resistor with resistance R connected to an AC source (diagram 1). If the AC source provides a voltage VR(t) = V0 cos(?t), what is the current IR(t) through the resistor as a function of time?
Express your answer in terms of V0, R, ?, and t.
IR(t) =

Part B
Now consider an inductor with inductance L in an AC circuit (diagram 2). Assuming that the current in the inductor varies as IL(t) = I0 cos(?t), find the voltage VL(t) that must be driving the inductor.
Express your answer in terms of I0, L, ?, and t. Use the cosine function, not the sine function, in your answer.
VL(t) =

Part C
Again consider an inductor with inductance L connected to an AC source. If the AC source provides a voltage VL(t) = V0 cos(?t), what is the current IL(t) through the inductor as a function of time?
Express your answer in terms of V0, L, ?, and t. Use the cosine function, not the sine function, in your answer.
IL(t) =

Added by Andre A.

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