Consider the circuit from P2 in PS2, now connected to an external source as shown in figure 2. The external source is an AC source with Vac(t) = V₁ cos(Nt + p). R, L, Vo, №, o are arbitrary positive constants. ³. 2 ^- R 0000

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**Text Transcription:**

Consider the circuit from P2 in PS2, now connected to an external source as shown in figure 2. The external source is an AC source with \( V_{AC}(t) = V_0 \cos(\Omega t + \phi) \). \( R, L, V_0, \Omega, \phi \) are arbitrary positive constants.

**Figure Description:**

Figure 2 illustrates an 'R+LC' circuit connected to an external source. The diagram includes:

- An AC voltage source on the left, represented by a circle with a sine wave inside, symbolizing the alternating nature of the voltage.
- A resistor labeled \( R \) in series with the AC source.
- A capacitor labeled \( C \) and an inductor labeled \( L \) in parallel with each other, forming an LC parallel circuit connected in series with the resistor.
- The AC source is characterized by the equation \( V_{AC}(t) = V_0 \cos(\Omega t + \phi) \), indicating a cosine wave with amplitude \( V_0 \), angular frequency \( \Omega \), and phase shift \( \phi \).

This configuration is commonly studied in circuits involving alternating current analysis where resistor, inductor, and capacitor components interact with an AC source.
Transcribed Image Text:**Text Transcription:** Consider the circuit from P2 in PS2, now connected to an external source as shown in figure 2. The external source is an AC source with \( V_{AC}(t) = V_0 \cos(\Omega t + \phi) \). \( R, L, V_0, \Omega, \phi \) are arbitrary positive constants. **Figure Description:** Figure 2 illustrates an 'R+LC' circuit connected to an external source. The diagram includes: - An AC voltage source on the left, represented by a circle with a sine wave inside, symbolizing the alternating nature of the voltage. - A resistor labeled \( R \) in series with the AC source. - A capacitor labeled \( C \) and an inductor labeled \( L \) in parallel with each other, forming an LC parallel circuit connected in series with the resistor. - The AC source is characterized by the equation \( V_{AC}(t) = V_0 \cos(\Omega t + \phi) \), indicating a cosine wave with amplitude \( V_0 \), angular frequency \( \Omega \), and phase shift \( \phi \). This configuration is commonly studied in circuits involving alternating current analysis where resistor, inductor, and capacitor components interact with an AC source.
(d) Find an expression for the maximum current in the inductor over one cycle of the external AC source: \( I_{L,\text{max}} \). Does it depend on \( \phi \)?

Hints: 
i/ you do not need to take any derivatives to answer this question. 
ii/ make sure that \( I_{L,\text{max}} \) has units of current.
Transcribed Image Text:(d) Find an expression for the maximum current in the inductor over one cycle of the external AC source: \( I_{L,\text{max}} \). Does it depend on \( \phi \)? Hints: i/ you do not need to take any derivatives to answer this question. ii/ make sure that \( I_{L,\text{max}} \) has units of current.
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