7. In a series RL circuit, under what circumstances would $$ \phi $$ be $$ 0^{\circ} $$ or $$ 90^{\circ} $$ ? ( $$ \phi $$ will be zero if the circuit is purely resistive) ( $$ \phi $$ will be $$ 90^{\circ} $$ if the circuit is purely inductive). 8. In a series RC circuit, under what circumstances would $$ \phi $$ be exactly $$ 0^{\circ} $$ or $$ -90^{\circ} $$ ? ( $$ \phi $$ will be zero if the circuit is purely resistive) ( $$ \phi $$ will be $$ -90^{\circ} $$ if the circuit is purely capacitive).

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Your answers to both questions are **correct**. Here's a detailed explanation for each:

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### **7. Series RL Circuit Phase Angle ($$ \phi $$)**

- **Purely Resistive Circuit ($$ \phi = 0^{\circ} $$)**
  - **Explanation:** In a purely resistive circuit, the voltage and current are **in phase**. This means there is no phase difference between them, resulting in a phase angle ($$ \phi $$) of **0 degrees**.
  
- **Purely Inductive Circuit ($$ \phi = 90^{\circ} $$)**
  - **Explanation:** In a purely inductive circuit, the **voltage leads the current by 90 degrees**. This phase difference is due to the property of inductors to oppose changes in current, causing the current to lag behind the voltage. Hence, $$ \phi = 90^{\circ} $$.

**Summary:**
- $$ \phi = 0^{\circ} $$ when the circuit is purely resistive.
- $$ \phi = 90^{\circ} $$ when the circuit is purely inductive.

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### **8. Series RC Circuit Phase Angle ($$ \phi $$)**

- **Purely Resistive Circuit ($$ \phi = 0^{\circ} $$)**
  - **Explanation:** Similar to the RL circuit, in a purely resistive RC circuit, the voltage and current are **in phase**, resulting in a phase angle ($$ \phi $$) of **0 degrees**.
  
- **Purely Capacitive Circuit ($$ \phi = -90^{\circ} $$)**
  - **Explanation:** In a purely capacitive circuit, the **current leads the voltage by 90 degrees**. Capacitors store and release energy, causing the voltage to lag behind the current. Therefore, the phase angle $$ \phi = -90^{\circ} $$.

**Summary:**
- $$ \phi = 0^{\circ} $$ when the circuit is purely resistive.
- $$ \phi = -90^{\circ} $$ when the circuit is purely capacitive.

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These phase relationships are fundamental in understanding AC circuit behavior and are essential for analyzing and designing circuits involving resistors, inductors, and capacitors.
In a series RL circuit, $$ \phi = 0^{\circ} $$ when the circuit is purely resistive and $$ \phi = 90^{\circ} $$ when it's purely inductive. In a series RC circuit, $$ \phi = 0^{\circ} $$ when the circuit is purely resistive and $$ \phi = -90^{\circ} $$ when it's purely capacitive.

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