Direct and Alternating Currents

Coulomb's Force

Coulomb Law Formula Discussion

University Physics Volume 3 - 1.3 Refraction - EXAMPLE 1.2

EXAMPLE 1.2
Determining the Index of Refraction

Find the index of refraction for medium 2 in Figure (a), assuming medium 1 is air
and given that the incident angle is
°
and the angle of refraction is
°.

You can change angles and the result will be calculated for your angles.

Strategy
The index of refraction for air is taken to be 1 in most cases (and up to four significant figures, it is 1.000). Thus, n₁ = 1.00 here. From the given information, θ₁ = 30.0° and θ₂ = 22.0°.
With this information, the only unknown in Snell’s law is n₂, so we can use Snell’s law to find it.

Solution
From Snell’s law, we have
n₁ sin θ₁ = n₂ sin θ₂

n₂ = n₁ sinθ₁ / sinθ₂.
Entering known values,
n₂ = 1.00 sin 30.0° / sin 22.0° = 0.500 / 0.375 = 1.33

What is C?

The angular frequency of the oscillations in an LC circuit is .0×10³ rad/s.

If L= H, what is C?

Solution:

C=µC

What is the maximum current flowing through the circuit?

In an LC circuit, the self-inductance is
L=.0×10⁻² H
and the capacitance is
C=.0×10⁻⁶ F.

At t=0, all of the energy is stored in the capacitor, which has a charge
q=×10⁻⁵ C. 

(a) What is the angular frequency ω of the oscillations in the circuit?

(b) What is the maximum current I₀ flowing through the circuit?

(c) How long does it take the capacitor to become completely discharged? t_d=?

(d) What is the capacitor charge in µC when time t = ×10⁻⁴s?

Solution:

(b) The current is at its maximum when all the energy is stored in the inductor. From the law of energy conservation:


(c) The capacitor becomes completely discharged in one-fourth of a cycle, or during a time T/4, where T is the period of the oscillations. Since

(d) q=q₀ × cos(ω t)



 ω= rad/s
  I₀= A
t_d= s
q(t)= µC

LC Angular Frequency of the Oscillations in the Circuit

In an LC circuit, the self-inductance is
L=.0×10⁻² H
and the capacitance is
C=.0×10⁻⁶ F.

At t=0, all of the energy is stored in the capacitor, which has a charge
q=×10⁻⁵ C. 

What is the angular frequency of the oscillations in the circuit?

 ω= rad/s