Skip to main content
Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 30 - Inductance, Electromagnetic Oscillations, and AC CircuitsProblem 9
Chapter 29, Problem 9

A coil has 3.25-Ω resistance and 440-mH inductance. If the current is 3.00 A and is increasing at a rate of 3.15 A/s, what is the potential difference across the coil at this moment?

Verified step by step guidance
1
Identify the components of the coil: The coil has a resistance \( R = 3.25 \, \Omega \), an inductance \( L = 440 \, \text{mH} = 0.440 \, \text{H} \), a current \( I = 3.00 \, \text{A} \), and a rate of change of current \( \frac{dI}{dt} = 3.15 \, \text{A/s} \).
Recall the formula for the potential difference across a coil, which is the sum of the resistive voltage drop and the inductive voltage drop: \( V = IR + L \frac{dI}{dt} \).
Substitute the given values into the formula: \( V = (3.00)(3.25) + (0.440)(3.15) \).
Simplify the terms: Calculate the resistive voltage drop \( IR \) and the inductive voltage drop \( L \frac{dI}{dt} \) separately.
Add the two contributions to find the total potential difference \( V \). Ensure the units are consistent throughout the calculation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ohm's Law

Ohm's Law states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, given by the formula V = IR, where R is the resistance. This principle is fundamental in electrical circuits, allowing us to calculate the voltage drop across resistive components when the current is known.
Recommended video:
Guided course
03:07
Resistance and Ohm's Law

Inductance and Inductive Reactance

Inductance is a property of an electrical component, typically a coil, that opposes changes in current. The inductive reactance (XL) can be calculated using the formula XL = L(dI/dt), where L is the inductance and dI/dt is the rate of change of current. This concept is crucial for understanding how inductors behave in AC circuits and during transient states.
Recommended video:
Guided course
12:59
Mutual Induction

Total Voltage in an RL Circuit

In a series RL circuit, the total voltage across the coil is the sum of the voltage across the resistor and the voltage across the inductor. This can be expressed as V_total = V_R + V_L, where V_R = IR and V_L = L(dI/dt). Understanding this relationship is essential for calculating the potential difference across the coil when both resistance and inductance are present.
Recommended video:
Guided course
05:29
Total Internal Reflection
Related Practice
Textbook Question

At a given instant, a 2.4-A current flows in the wires connected to a parallel-plate capacitor. What is the rate at which the electric field is changing between the plates if the square plates are 1.60 cm on a side?

3
views
Textbook Question

(II) If the solenoid in Fig. 29–47 is being pulled away from the loop shown, in what direction is the induced current in the loop? Explain.

1
views
Textbook Question

(III) A toroid has a rectangular cross section as shown in Fig. 30–26. Show that the self-inductance is


L=μ0N2h2πlnr2r1L = \(\frac{\mu_0 N^2 h}{2\pi}\) \(\ln\) \(\frac{r_2}{r_1}\)


where N is the total number of turns and r₁, r₂ and h are the dimensions shown in Fig. 30–26. [Hint: Use Ampère’s law to get B as a function of r inside the toroid, and integrate.]


2
views
Textbook Question

(III) A long straight wire and a small rectangular wire loop lie in the same plane, Fig. 30–25. Determine the mutual inductance in terms of 𝓁₁, 𝓁₂, and w. Assume the wire is very long compared to 𝓁₁, 𝓁₂, and w, and that the rest of its circuit is very far away compared to 𝓁₁, 𝓁₂, and w.

2
views
Textbook Question

The magnetic field inside an air-filled solenoid 38.0 cm long and 2.10 cm in diameter is 0.720 T. Approximately how much energy is stored in this field?

1
views
Textbook Question

(II) Part of a single rectangular loop of wire with dimensions shown in Fig. 29–49 is situated inside a region of uniform magnetic field of 0.650 T. The total resistance of the loop is 0.250 Ω. Calculate the force required to pull the loop from the field (to the right) at a constant velocity of 3.40 m/s. Neglect gravity.

2
views