Chapter 31: Problem 42
A toroidal solenoid has 2900 closely wound turns, cross-sectional area 0.450 cm\(^2\), mean radius 9.00 cm, and resistance \(R\) = 2.80 \(\Omega\). Ignore the variation of the magnetic field across the cross section of the solenoid. What is the amplitude of the current in the solenoid if it is connected to an ac source that has voltage amplitude 24.0 V and frequency 495 Hz?
Short Answer
Step by step solution
Convert Cross-Sectional Area to Meters Squared
Calculate the Inductance (L) of the Solenoid
Evaluate the Inductive Reactance (X_L)
Calculate the Impedance (Z) of the Circuit
Determine the Amplitude of the Current
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Inductance Calculation
- \( \mu_0 \) is the permeability of free space, which is a constant \( 4\pi \times 10^{-7} \text{ T m/A} \).
- \( N \) is the total number of turns in the solenoid.
- \( A \) is the cross-sectional area in square meters.
- \( r \) is the mean radius of the solenoid in meters.
AC Circuit Analysis
Inductive Reactance
- \( f \) is the frequency of the AC source in hertz (Hz).
- \( L \) is the inductance in henrys (H).
Impedance Calculation
- \( R \) is the resistance in ohms (Ω).
- \( X_L \) is the inductive reactance calculated previously.