30. Induction and Inductance

A voltage $v\left(t\right)=10cos\left(2000\omega t\right)$ is applied to a $100-\mathrm{mH}$ inductor. What is the expression for the current $i\left(t\right)$ through the inductor (assume zero initial current)?

Which of the following expressions gives the energy stored in an ideal inductor with inductance $L$ carrying a current $I$?

In an $RL$ circuit with a resistor and an inductor in series connected to a constant voltage source, what effect does increasing the inductance of the inductor have on the rate at which the current reaches its maximum steady-state value after the circuit is closed?

Which of the following expressions correctly gives the inductance of a closely packed solenoidal coil of length $l$, cross-sectional area $A$, number of turns $N$, and permeability $\mu$ of the core material?

A 30mH inductor carries a current of 500mA. If the circuit is opened and the current stops over a period of 3.0μs, what potential develops across the inductor?

A toroidal solenoid has mean radius 12.0 cm and crosssectional area 0.600 cm². How many turns does the solenoid have if its inductance is 0.100 mH?

The inductor shown in Fig. E30.11 has inductance 0.260 H and carries a current in the direction shown. The current is changing at a constant rate. The potential between points a and b is V_ab = 1.04 V, with point a at higher potential. Is the current increasing or decreasing?

When the current in a toroidal solenoid is changing at a rate of 0.0260 A/s, the magnitude of the induced emf is 12.6 mV. When the current equals 1.40 A, the average flux through each turn of the solenoid is 0.00285 Wb. How many turns does the solenoid have?

What is the potential difference across a 10 mH inductor if the current through the inductor drops from 150 mA to 50 mA in 10 μs? What is the direction of this potential difference? That is, does the potential increase or decrease along the direction of the current?

CALC FIGURE P30.67 shows the potential difference across a 20 mH inductor. The current through the inductor at t = 0 ms is 0.25 A. What is the current at t = 10 ms?

CALC The current through inductance L is given by $I=I_0{e}^{-t/\tau }$. Evaluate ΔV_L at t = 0, 1.0, and 3.0 ms if L = 20 mH, I₀ = 50 mA, and $\tau$ = 1.0 ms.

CALC The current through inductance L is given by $I=I_0{e}^{-t/\tau }$. Find an expression for the potential difference ΔV_L across the inductor.

How much energy is stored in a 3.0-cm-diameter, 12-cm-long solenoid that has 200 turns of wire and carries a current of 0.80 A?

BIO MRI (magnetic resonance imaging) is a medical technique that produces detailed 'pictures' of the interior of the body. The patient is placed into a solenoid that is 40 cm in diameter and 1.0 m long. A 100 A current creates a 5.0 T magnetic field inside the solenoid. To carry such a large current, the solenoid wires are cooled with liquid helium until they become superconducting (no electric resistance). How much magnetic energy is stored in the solenoid? Assume that the magnetic field is uniform within the solenoid and quickly drops to zero outside the solenoid.

Assuming the Earth’s magnetic field averages about 0.50 x 10^-4 T near the surface of the Earth, estimate the total energy stored in this field in the first 5.0 km above the Earth’s surface.