An 820 turn wire coil of resistance 28.0 Q is placed around a 12500 turn solenoid, 7.60 cm long, as shown in the figure below. Both coil and solenoid have cross-sectional areas of 1.20 x 10-4 m². 14.0 2 W 60,0 V 12 500 turns. Rc 820 turns. (a) How long does it take the solenoid current to reach 63.2% of its maximum value? ms (b) Determine the average back emf caused by the self-inductance of the solenoid during this interval. (c) Determine the average rate of change in magnetic flux through the coil during this interval. V (d) Determine the magnitude of the average induced current in the coil.

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## Inductive Circuit Analysis

An 820-turn wire coil of resistance **28.0 Ω** is placed around a 12,500-turn solenoid, **7.60 cm** long, as shown in the figure below. Both coil and solenoid have cross-sectional areas of **1.20 × 10⁻⁴ m²**.

### Diagram Description

- The diagram shows a solenoid connected in a circuit with a power supply of **60.0 V**.
- The solenoid has **12,500 turns**.
- An additional coil with **820 turns** and resistance **28.0 Ω** is wound around the solenoid.
- The circuit includes a resistor of **14.0 Ω**.
- Current flows from the power supply, through the resistor, and into the solenoid. The switch **S** is used to control the circuit.

### Questions and Calculations

(a) **How long does it take the solenoid current to reach 63.2% of its maximum value?**

- Answer in ms: ▢

(b) **Determine the average back emf caused by the self-inductance of the solenoid during this interval.**

- Answer in V: ▢

(c) **Determine the average rate of change in magnetic flux through the coil during this interval.**

- Answer in V: ▢

(d) **Determine the magnitude of the average induced current in the coil.**

- Answer in A: ▢

These questions involve applications of electromagnetic induction, analyzing time constants, back electromotive force (emf), and induced currents in circuits.
Transcribed Image Text:## Inductive Circuit Analysis An 820-turn wire coil of resistance **28.0 Ω** is placed around a 12,500-turn solenoid, **7.60 cm** long, as shown in the figure below. Both coil and solenoid have cross-sectional areas of **1.20 × 10⁻⁴ m²**. ### Diagram Description - The diagram shows a solenoid connected in a circuit with a power supply of **60.0 V**. - The solenoid has **12,500 turns**. - An additional coil with **820 turns** and resistance **28.0 Ω** is wound around the solenoid. - The circuit includes a resistor of **14.0 Ω**. - Current flows from the power supply, through the resistor, and into the solenoid. The switch **S** is used to control the circuit. ### Questions and Calculations (a) **How long does it take the solenoid current to reach 63.2% of its maximum value?** - Answer in ms: ▢ (b) **Determine the average back emf caused by the self-inductance of the solenoid during this interval.** - Answer in V: ▢ (c) **Determine the average rate of change in magnetic flux through the coil during this interval.** - Answer in V: ▢ (d) **Determine the magnitude of the average induced current in the coil.** - Answer in A: ▢ These questions involve applications of electromagnetic induction, analyzing time constants, back electromotive force (emf), and induced currents in circuits.
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