Ch 3: Voltage and Current Laws

Question 1

What does it mean for elements to be

in Parallel?

Answer 1

The elements have a common voltage across them.

Question 2

Resistors in Series:

Equivalent Resistance

Answer 2

The sum of the resitances:

R_eq = ∑ R_i

Question 3

Resistors in Parallel:

Equivalent Resistance

Answer 3

Inverse of the sum of the inverse of resistances.

1/R_eq = ∑ 1/R_i

Another way of considering it is that the Equivalent Conductance is the Sum of conductances

G_eq = ∑ G_i

Question 4

What does it mean for elements to be

“in series”?

Answer 4

The elements are “lined up” and carry the same current.

Question 5

What is a

Lumped Parameter Network?

Answer 5

A network that appears as a number of simple elements,

and a set of connecting leads.

Question 6

Current Division:

Current Equations for two resistors

Answer 6

i₁ = i * R₁/(R₁+R₂)

i₂ = i * R2/(R₁+R₂)

Question 7

Current Division:

General Equation

Answer 7

i_k = i * (1/R_k) / ∑(1/R_i)

or

i_k = i * G_k/∑G_i

Question 8

Equivalent Resistance of

two Parallel Resistors

Answer 8

R_eq = R₁R₂ / (R₁ + R₂)

Question 9

Combining Sources:

Basic Rules (4)

Answer 9

Series Voltage Sources -> Sum of Voltage Sources

Parallel Current Sources -> Sum of Current Sources

Parallel Voltage Sources -> Physically impossible, unless voltage is the same

Series Current Sources -> Physically impossible unless current is the same

Question 10

Three Kinds of Ground

Answer 10

Earth Ground:

Physically connected to the earth ground, represented by three horizontal lines

Signal Ground:

Acts as ground for the circuit, but may not actually be grounded

Chassis Ground:

Connected to a large piece of metal, such as a car chassis. Slanted Vertical lines

Question 11

Voltage Division:

General Equation

Answer 11

For a set of N resistors in series, voltage across any of the resistors is given by:

v_k = v * R_k / ∑R_i