Q: A circuit consists of three resistors: $$R_1 = 2$$\ \Omega$$, R_2$ = 4\ \Omega$$, and $$R_3 = 6$$\ \Omega$$. R_1$ and R_2$ are connected in parallel, and their combination is connected in series with R_3$. What is the total resistance of the circuit?

$$R_{\text{total}} = 4.67\ \Omega$$

Question 1

A circuit consists of three resistors: $$R_1 = 2$$\ \Omega$$, R_2$ = 4\ \Omega$$, and $$R_3 = 6$$\ \Omega$$. R_1$ and R_2$ are connected in parallel, and their combination is connected in series with R_3$. What is the total resistance of the circuit?

Accepted Answer

$$R_{	ext{total}} = 4.67\ \Omega$$

Question 2

A transformer has 100 turns on its primary coil and 400 turns on its secondary coil. If the input voltage is $$120\ 	ext{V}$$, what is the output voltage (assuming an ideal transformer)?

Accepted Answer

$$V_s = 480\ 	ext{V}$$

Question 3

A proton moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$Which of the following correctly gives the radius of the circular path of the proton?

Accepted Answer

$$r = \dfrac{mv}{|q|B}$$

Question 4

A 60 Hz electromagnetic wave travels through air. If its wavelength is $$5\ 	ext{m}$$, what is the speed of the wave?

Accepted Answer

$$v = 300\ 	ext{m/s}$$

Question 5

In an RLC circuit, the impedance is given by $$Z = \sqrt{R^2$ + \left(\omega L - \dfrac{1}{\omega C}\$$right)^2$$}. If$$ $$R = 10\ \Omega$$, $$L = 0.1\ 	ext{H}$$, $$C = 100\ \mu	ext{F}$$, and $$\omega = 100\ 	ext{rad/s}$$, what is the impedance?

Accepted Answer

$$Z = 20\ \Omega$$

Question 6

A string of length $$L is $$fixed at both ends. Which of the following gives the frequency of the third harmonic?

Accepted Answer

$$f_3$$ = \dfrac{3v}{2L}$$

Question 7

A rectangular loop of wire with area $$A is $$placed in a uniform magnetic field $$B$$ such that the angle between $$\vec{B}$$ and the normal to the loop is $$	heta. $$What is the magnetic flux through the loop?

Accepted Answer

$$\Phi_B = BA\cos	heta$$

Question 8

A long straight wire carries a current $$I. $$What is the magnitude of the magnetic field at a distance $$r$$ from the wire?

Accepted Answer

$$B = \dfrac{\mu_0$ I}{2\pi r}$$

Question 9

A dipole antenna emits electromagnetic waves. Which statement is correct about the orientation of the electric field ($$\vec{E}) $$and magnetic field ($$\vec{B}) in $$the emitted wave?

Accepted Answer

$$\vec{E} is $$perpendicular to $$\vec{B}$$, and both are perpendicular to the direction of propagation.

Question 10

A current-carrying wire segment of length $$L is $$placed in a uniform magnetic field $$\vec{B}$$, perpendicular to the wire. What is the magnitude of the force on the wire?

Accepted Answer

$$F = ILB$$

Question 11

A generator coil rotates in a magnetic field, causing the magnetic flux through the coil to change with time. According to Faraday’s Law, what is the induced EMF in the coil?

Accepted Answer

$$E = -\dfrac{d\Phi_B}{dt}$$

Question 12

A 120 V power line is stepped down to 12 V using a transformer to power a device. If the device draws 5 A, what is the current in the primary coil (assuming an ideal transformer)?

Accepted Answer

$$I_p = 0.5\ 	ext{A}$$

Question 13

A charged particle enters a region with a uniform magnetic field at an angle of $$90^\circ to $$the field. Which force acts on the particle, and what is its direction?

Accepted Answer

The Lorentz force, perpendicular to both the velocity and the magnetic field.

Question 14

In a standing wave on a string fixed at both ends, what is the distance between two adjacent nodes?

Accepted Answer

$$\dfrac{\lambda}{2}$$

Question 15

A wire loop is moved rapidly out of a region with a strong magnetic field. According to Lenz’s Law, what is the direction of the induced current in the loop?

Accepted Answer

It flows to increase the magnetic flux through the loop.

Question 16

A series RLC circuit is driven at its resonance frequency. Which of the following statements is true?

Accepted Answer

The impedance is minimized and equals the resistance $$R.$$

Question 17

A 10 m long wire carries a current of 2 A and is placed in a uniform magnetic field of $$0.5\ 	ext{T}$$ perpendicular to the wire. What is the magnitude of the force on the wire?

Accepted Answer

$$F = 20\ 	ext{N}$$

Question 18

Which of the following best describes the energy oscillations in an RLC circuit?

Accepted Answer

Energy oscillates between the capacitor and the inductor.

Question 19

A wave on a string is described by $$y(x, t) = A \sin(kx - \omega t). $$What is the speed of the wave?

Accepted Answer

$$v = \dfrac{\omega}{k}$$

Question 20

A current loop is placed near a long straight current-carrying wire. What is the net force on the loop?

Accepted Answer

It depends on the orientation and position of the loop relative to the wire.

PHYS E-1bx: Midterm 2 Study Guide – Circuits, Electromagnetism, and Waves

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