Q: Planck's constant $$h is $$approximately:

$$6.626 \times 10$$^{-34}$$ \text{ J s}$$

Q: The speed of electromagnetic waves in vacuum is:

$$c = 2.998 \times 10^8$ \text{ m/s}$$

Question 1

Which of the following correctly expresses the self-induced emf in a coil with inductance $$L$$ and changing current $$\frac{dI}{dt}$$?

Accepted Answer

$$\varepsilon = -L \frac{dI}{dt}$$

Question 2

A solenoid of length $$l$$, cross-sectional area $$A$$, and $$N$$ turns has a self-inductance given by which formula?

Accepted Answer

$$L = \mu_0$ \frac{N^2$ A}{l}$$

Question 3

In an AC circuit with a resistor $$R$$, inductor $$L$$, and capacitor $$C in $$series, what is the expression for the total impedance $$Z$$?

Accepted Answer

$$Z = \sqrt{R^2$ + (\omega L - \frac{1}{\omega C})^2$}$$

Question 4

If the phase angle $$\phi in an $$RLC circuit is zero, what does this imply about the relationship between $$\omega L$$ and $$\frac{1}{\omega C}$$?

Accepted Answer

$$\omega L = \frac{1}{\omega C}$$

Question 5

The effective (rms) value of a sinusoidal current with amplitude $$I_0 is$$:

Accepted Answer

$$I_{rms} = \frac{I_0$}{\sqrt{2}}$$

Question 6

In an RLC circuit, resonance occurs when:

Accepted Answer

$$\omega L = \frac{1}{\omega C}$$

Question 7

What is the average power delivered to a resistor $$R in an AC $$circuit with rms voltage $$V_{rms}$$?

Accepted Answer

$$P_{avg} = \frac{V_{rms}^2}{R}$$

Question 8

A circuit has $$R = 100 \Omega$$, $$X_L = 200 \Omega$$, and $$X_C = 50 \Omega. $$What is the impedance $$Z$$?

Accepted Answer

$$Z = \sqrt{100^2$ + (200 - 50)^2$} = \sqrt{100^2$ + 150^2$}$$

Question 9

Planck's constant $$h is $$approximately:

Accepted Answer

$$6.626 	imes 10$$^{-34}$$ 	ext{ J s}$$

Question 10

The energy of a photon with frequency $$f is $$given by:

Accepted Answer

$$E = h f$$

Question 11

A photon has a wavelength $$\lambda. $$What is its energy?

Accepted Answer

$$E = \frac{h c}{\lambda}$$

Question 12

The speed of electromagnetic waves in vacuum is:

Accepted Answer

$$c = 2.998 	imes 10^8$ 	ext{ m/s}$$

Question 13

Total internal reflection occurs when the angle of incidence is greater than the critical angle. What is the formula for the critical angle $$	heta_c$$ between two media with indices $$n_1$$ and $$n_2$$ ($$n_1$$ \u003e $$n_2$$)?

Accepted Answer

$$\sin 	heta_c = \frac{n_2$}{n_1$}$$

Question 14

Which of the following best describes the phenomenon of polarization?

Accepted Answer

Polarization is when the electric field vectors of an EM wave are oriented in the same direction perpendicular to the direction of propagation.

Question 15

A laser emits light of wavelength $$500 	ext{ nm}. $$What is the energy of each photon?

Accepted Answer

$$E = \frac{6.626 	imes 10$$^{-34}$$ 	imes 3.00 	imes 10^8$}{500 	imes 10$$^{-9}$$} 	ext{ J}$$

Question 16

In an AC circuit, the average power delivered to a load is zero when:

Accepted Answer

The phase angle $$\phi is$$ $$90^\circ$$ and the load is purely reactive.

Question 17

Which formula gives the wavelength $$\lambda of a $$photon in terms of its energy $$E$$?

Accepted Answer

$$\lambda = \frac{h c}{E}$$

Question 18

A capacitor in an AC circuit has reactance $$X_C. $$What is the formula for $$X_C$$?

Accepted Answer

$$X_C = \frac{1}{\omega C}$$

Question 19

If the rms voltage across a $$50 \Omega$$ resistor is $$100 	ext{ V}$$, what is the average power dissipated?

Accepted Answer

$$P_{avg} = \frac{100^2$}{50} = 200 	ext{ W}$$

Key Topics and Formulas: Self-Inductance, AC Circuits, and Electromagnetic Radiation

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