Deck 2: Circuit Laws

Question 1

the equivalent resistance between terminals a and b of the circuit shown below.

Answer 1

clear all;format long;
R1=10000;R2=33000;R3=88000;R4=19000;R5=70000;R6=12500;R7=30000;R8=42000;
Ra=P([R7,R8])
Rb=R6+Ra
Rc=P([R5,Rb])
Rd=R4+Rc
Re=P([R2,R3,Rd])
Req=R1+Re

Answer:
Ra =17500
Rb =30000
Rc =21000
Rd =40000
Re =15000
Req =25000

Question 2

the circuit shown below, find the currents I₁,I₂, and I₃. Also, find the powers on R₁,R₂, R₃,and V_s and state whether power is absorbed or released by each element.

Answer 2

Application of Ohm's law yields

Question 3

current through resistor R₆ in the circuit shown below is 2 mA, that is,I₆ = 2 mA.
(a) Use Ohm's law to find the voltage V₄ across R₆.
(b) Use Ohm's law to find the current I₅ through R₅.
(c) Use KCL to find the current I₄ through R₄.
(d) Use Ohm's law to find the voltage V₃ across R₄.
(e) Use KVL to find the voltage V₂ across R₃.
(f) Use Ohm's law to find the current I₃ through R₃.
(g) Use Ohm's law to find the current I₂ through R₂.
(h) Use KCL to find the current I₁ through R₁.
(i) Use Ohm's law to find the voltage V₁ across R₁.
(j) Use KVL to find the voltage V_s.

Answer 3

Question 4

circuit is shown in Figure 1. In this figure,
(a) Label all the nodes (1, 2, 3, ...) in the circuit excluding the ground node which is already
labeled as 0.
(b) How many nodes are there?
(c) How many simple nodes are there?
(d) How many essential nodes are there?
(e) How many branches are there?
(f) How many meshes are there? List all meshes.
(g) How many loops (including meshes) are there?
(h) List all loops that are not meshes. Figure 1

Question 5

the circuit shown below,
(a) Find R_a = R₅ || R₆ and R_b = R₃ || R₄.
(b) Redraw the circuit consisting of V_s, R₁, R_b, R₄, and R_a. Find the equivalent resistance R_eq
seen from the voltage source.
(c) Find the current I1 through R₁, R_b, R₄, and R_a.
(d) Find the voltage across R₁, voltage across R_b, voltage across R₄, and voltage across R_a
(e) Find the voltage V₁, voltage V₂, and voltage V₃.
(f) Find the currents I₂, I₃, I₅ and I₆.

Question 6

the equivalent resistance between terminals a and b of the circuit shown below.

Question 7

Find V₁, V₂, and V₃ in the circuit shown below.

Question 8

the circuit shown below,
(a) Find R_a = R₇ || R₈.
(b) Find R_b = R₆ + R_a.
(c) Find R_c = R₅ || R_b.
(d) Find R_d = R₂ || R₃.
(e) Redraw the circuit consisting of V_s, R₁, R_d, R₄, and Rc. Find the equivalent resistance R_eq
seen from the voltage source.
(f) Find the current I₁ through R₁, Rd, R₄, and R_c.
(g) Find the voltage across R₁, voltage across R_d, voltage across R₄, and voltage across R_c.
(h) Find the voltage V₁, voltage V₂, and voltage V₃.
(i) Find the currents I₅ and I₆.
(j) Find the voltage V₄, and currents I₇ and I₈.

Question 9

the equivalent resistance between terminals a and b of the circuit shown below.

Question 10

the circuit shown below,
(a) Find the equivalent resistances R_a = R₃ || R₄, R_b = R₅ || R₆, and R_c = R_a + R_b.
(b) Redraw the circuit consisting of Is, R₁, R₂, R_c.
(c) Use the current divider rule to find the currents I₁, I₂, I_c.
(d) Use the current divider rule to find the currents I₃, I₄, I₅, I₆.
(e) Find the voltages V₁, V₂.