Competitive Physics: Thermodynamics, Electromagnetism and Relativity

Wang Jinhui

Chapter 9 DC Circuits - all with Video Answers

Educators

Chapter Questions

Problem 1

Two resistors $R_1$ and $R_2$ are connected in series with a constant voltage source. We do not know the exact values of $R_1$ and $R_2$ but only their ratio $r=\frac{R_1}{R_2}$. If we subsequently connect a certain resistor in parallel to $R_2$, the current flowing through $R_1$ changes by $\Delta I_1$. What is the current flowing through the new resistor?

Nolwazi Dube

Numerade Educator

02:08

Problem 2

Find the current through the $2 \Omega$ resistor in the circuit below.
(GRAPH CAN'T COPY)

Ekaveera Kumar

Numerade Educator

11:33

Problem 3

Determine currents $I_1$ and $I_2$ in the circuit below.
(GRAPH CAN'T COPY)

Hemraj Kumawat

Numerade Educator

01:07

Problem 4

Determine the current flowing through the battery with $\operatorname{emf} \varepsilon$ in the circuit below.
(GRAPH CAN'T COPY)

Narayan Hari

Numerade Educator

04:01

Problem 5

Show that no current flows in every branch of the circuit below. All batteries are identical and have $\operatorname{emf} \varepsilon$.
(GRAPH CAN'T COPY)

Ren Jie Tuieng

Numerade Educator

02:17

Problem 6

Determine current $I$ in the circuit below via nodal analysis.
(GRAPH CAN'T COPY)

Varsha Aggarwal

Numerade Educator

03:11

Problem 7

Exploiting the principle of superposition, determine the currents through all resistors on the circuit below.
(GRAPH CAN'T COPY)

Ze-Han Lee

Numerade Educator

02:19

Problem 8

Find the equivalent resistance of the infinite grid of resistors $R$ between adjacent nodes $\mathrm{A}$ and $\mathrm{B}$ if the resistor $R$ between $\mathrm{A}$ and $\mathrm{B}$ were replaced by a resistor $R^{\prime}$ instead.

Prem Bijarniya

Numerade Educator

01:00

Problem 9

Find the equivalent resistances between nodes 1, 9 and nodes 1,5 . All resistors are identical and possess resistance $R$.
(GRAPH CAN'T COPY)

Sheryl Ezze

Numerade Educator

09:27

Problem 10

A wire of resistivity $\rho$ and cross sectional area $A$ is bent into a tetrahedron as shown below. If all sides of the tetrahedron are of length $l$, find the equivalent resistance between points $\mathrm{A}$ and $\mathrm{M}$ which is the midpoint of $\mathrm{BC}$.
(GRAPH CAN'T COPY)

Mrinal Rana

Numerade Educator

02:40

Problem 11

Twenty identical resistors $R$ are connected as shown in the figure below. Calculate the equivalent resistance between points (a) A and B (b) A and C (c) A and D.
(GRAPH CAN'T COPY)

Mederic Rodriguez

Numerade Educator

06:36

Problem 12

Determine the equivalent resistance of the infinite ladder below between terminals A and B. The resistors in each section of the ladder (except the left-most one) have $k$ times the resistance of those in the preceding section. Verify your answer in the limit $k \rightarrow \infty$.
(GRAPH CAN'T COPY)

Ren Jie Tuieng

Numerade Educator

01:01

Problem 13

An unknown circuit, consisting of independent emf sources and resistors, is placed into a black box with two terminals A and B. When an ideal ammeter is connected between A and $\mathrm{B}$, its reading is $I$. When a resistor $R$ is connected instead, the current through that resistor is $i$. What would be the reading $V$ of an ideal voltmeter connected to $\mathrm{A}$ and $\mathrm{B}$ ?

Khoobchandra Agrawal

Numerade Educator

04:43

Problem 14

Each line in the figure below represents a $1 \Omega$ resistor.
(a) Determine the equivalent resistance between $\mathrm{A}$ and $\mathrm{C}$.
(b) Determine the equivalent resistance between $\mathrm{B}$ and $\mathrm{C}$.
(c) If a voltage source of $10 \mathrm{~V}$ is connected between $\mathrm{A}$ and $\mathrm{C}$, what is the potential difference between $\mathrm{D}$ and $\mathrm{E}$ ?
(d) If a voltage source of $10 \mathrm{~V}$ is connected between $\mathrm{B}$ and $\mathrm{C}$, what is the potential difference between $B$ and $D$ ?
(GRAPH CAN'T COPY)

Ze-Han Lee

Numerade Educator

05:48

Problem 15

Find the equivalent resistance between points $\mathrm{A}$ and $\mathrm{B}$ in an infinite grid consisting of identical resistors $R$ arranged in hexagonal tiles.
(GRAPH CAN'T COPY)

Netra Sharma

University of Wisconsin - Milwaukee

03:08

Problem 16

There are 2018 nodes with a resistor $R$ connected between each pair of nodes. Find the equivalent resistance of the entire network between any two nodes.

Prem Bijarniya

Numerade Educator

03:16

Problem 17

Find the equivalent resistance between any two points in a cube of resistors by utilizing the principle of superposition.

Pritesh Ranjan

Numerade Educator

04:15

Problem 18

A piece of wire with cross sectional area $A$ and resistivity $\rho$ is bent into the equilateral triangle fractal below. Each successive triangle has half the side length of its predecessor triangle and the pattern repeats indefinitely. Find the equivalent resistance between points $\mathrm{A}$ and $\mathrm{B}$.
(GRAPH CAN'T COPY)

Saman Zulfiqar

Numerade Educator

05:48

Problem 19

Determine the equivalent resistance between vertices $\mathrm{A}$ and $\mathrm{B}$ in the figure below. All resistors have resistance $R$. Hint: make use of vertex $\mathrm{C}$.
(GRAPH CAN'T COPY)

Netra Sharma

University of Wisconsin - Milwaukee

07:00

Problem 20

By applying Thevenin's theorem, determine the current flowing through branch $\mathrm{AB}$ in the circuit below.
(GRAPH CAN'T COPY)

Kajal Gautam

Numerade Educator

01:56

Problem 21

$N$ batteries are connected in parallel, with their terminals oriented in the same direction. If the $i$ th battery has an emf $\varepsilon_i$ and internal resistance $r_i$ and if the entire set-up can be reduced to a single equivalent battery with emf $\varepsilon_{e q}$ and internal resistance $r_{e q}$ with respect to two terminals at the ends of a parallel branch, determine $\varepsilon_{e q}$ and $r_{e q}$.

Prem Bijarniya

Numerade Educator

01:00

Problem 22

Determine the resistor $r$ that should be connected across the two terminals in the figure below such that the power through it is maximal across all possible values of $r$.
(GRAPH CAN'T COPY)

Sheryl Ezze

Numerade Educator

06:13

Problem 23

Find the current $I$ in the circuit below.
(GRAPH CAN'T COPY)

M Hassan Anwar

Numerade Educator

01:00

Problem 24

Determine the equivalent resistance between two adjacent nodes in the middle row of the infinite network of identical resistors $R$ in the figure below. The circuit only extends to infinity in the horizontal direction.
(GRAPH CAN'T COPY)

Sheryl Ezze

Numerade Educator

02:55

Problem 25

The $N$ edges of a regular $N$-gon are constructed by $N$ resistors $R$. Furthermore, all $N$ vertices of the $N$-gon are connected to its geometric center O via spokes of resistance $2 R$. Determine the equivalent resistance of this set-up between a vertex and $\mathrm{O}$.

Mahipal Kumawat

Numerade Educator