Q: A parallel plate capacitor has plates of area $$A = 1\,\mathrm{m}^2$$ separated by $$d = 1\,\mathrm{mm}$$ and is connected to a $$120\,\mathrm{V}$$ battery. What is the capacitance of the capacitor? (Use $$\$$varepsilon_0$$ = 8.85 \times 10$$^{-12}$$\,\mathrm{F/m})$$

$$8.85 \times 10$$^{-9}$$\,\mathrm{F}$$

Question 1

A cylindrical wire of length $$l$$ and radius $$r$$ has resistance $$R. If $$the radius is doubled while the length remains the same, what happens to the resistance?

Accepted Answer

The resistance is reduced to one-fourth.

Question 2

A parallel plate capacitor has plates of area $$A = 1\,\mathrm{m}^2$$ separated by $$d = 1\,\mathrm{mm}$$ and is connected to a $$120\,\mathrm{V}$$ battery. What is the capacitance of the capacitor? (Use $$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$\,\mathrm{F/m})$$

Accepted Answer

$$8.85 	imes 10$$^{-9}$$\,\mathrm{F}$$

Question 3

A charged particle moves in a region with both electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ perpendicular to each other. If the particle passes through the region undeflected, what is the relationship between its velocity $$v$$, $$E$$, and $$B$$?

Accepted Answer

$$v = E/B$$

Question 4

Three identical light bulbs, each with resistance $$R$$, are connected as shown: bulbs 2 and 3 are in series, and this combination is in parallel with bulb 1. What is the equivalent resistance of the circuit?

Accepted Answer

$$2R/3$$

Question 5

A capacitor is charged to $$Q at $$voltage $$V. If a $$dielectric with constant $$K is $$inserted while the capacitor is disconnected from the battery, what happens to the voltage across the capacitor?

Accepted Answer

It decreases by a factor of $$K.$$

Question 6

A resistor of resistance $$R is $$connected to a battery of voltage $$V. If $$the length of the resistor is doubled and the radius is halved, what happens to the resistance?

Accepted Answer

It increases by a factor of 8.

Question 7

A particle of mass $$m$$ and charge $$q$$ moves in a uniform magnetic field $$B$$ with velocity $$v$$ perpendicular to $$B. $$What is the radius of its circular path?

Accepted Answer

$$r = \dfrac{mv}{qB}$$

Question 8

Two capacitors $$C_1$$ and $$C_2$$ are connected in parallel. What is the equivalent capacitance?

Accepted Answer

$$C_1$$ + $$C_2$$

Question 9

A circuit contains two resistors $$R_1$$ and $$R_2 in $$parallel, connected to a voltage $$V. $$What is the total current supplied by the battery?

Accepted Answer

$$I = V \left( \dfrac{1}{R_1$} + \dfrac{1}{R_2$} \right)$$

Question 10

A capacitor with capacitance $$C is $$charged to voltage $$V. $$What is the energy stored in the capacitor?

Accepted Answer

$$U = \dfrac{1}{2}CV^2$

Question 11

A charged particle moves in a region with both electric and magnetic fields. If the electric force $$F_E$$ and magnetic force $$F_B$$ are equal in magnitude and opposite in direction, what happens to the particle's trajectory?

Accepted Answer

It moves in a straight line.

Question 12

If the voltage across a resistor is tripled, what happens to the current through the resistor?

Accepted Answer

It triples.

Question 13

A circuit contains three identical resistors $$R$$ arranged such that two are in series and this combination is in parallel with the third. What is the power dissipated in the resistor that is alone in parallel if the total voltage is $$V$$?

Accepted Answer

$$P = \dfrac{4V^2$}{9R}$$

Question 14

A capacitor is connected to a battery and charged. If the battery is removed and a dielectric is inserted, what happens to the stored energy in the capacitor?

Accepted Answer

It decreases by a factor of $$K.$$

Question 15

A particle of mass $$m$$ and charge $$q$$ passes through a region with electric field $$E$$ and magnetic field $$B$$ such that it is undeflected. If gravity is now included, what must be the new magnetic field $$B' to $$keep the particle undeflected?

Accepted Answer

$$B' = \dfrac{E}{v} + \dfrac{mg}{qv}$$

Question 16

Which of the following best describes the relationship between current $$I$$ and voltage $$V$$ for an ohmic material?

Accepted Answer

$$I \propto V$$

Question 17

Two capacitors $$C_1$$ and $$C_2$$ are connected in series. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = \dfrac{C_1$ C_2$}{C_1$ + C_2$}$$

Question 18

A resistor network consists of $$R_1$$ and $$R_2 in $$series, and this combination is in parallel with $$R_3. $$What is the total resistance?

Accepted Answer

$$R_{total} = \dfrac{(R_1$ + R_2$)R_3$}{R_1$ + R_2$ + R_3$}$$

Question 19

A charged particle moves in a magnetic field $$\vec{B}$$ with velocity $$\vec{v} at an $$angle $$	heta to$$ $$\vec{B}. $$What is the magnitude of the magnetic force on the particle?

Accepted Answer

$$F = qvB \sin 	heta$$

Electric Circuits, Magnetic Fields, and Capacitors: Exam Solutions and Study Guide

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