Basic Electric Circuits

A series connection has a single path from the battery, through each circuit element in turn, then back to the battery.

Resistors in Series

The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage.

Resistors in Series

From this we get the equivalent resistance (that single resistance that gives the same current in the circuit).

Resistors in Series

RT = 60

VT = 120 VIT = 2 A

Simple Series Circuit

Cut the resistor into three equal lengthsand then separate.

Resistors in Series

R1 = 20 R2 = 20 R3 = 20 V1 = 40 VV2 = 40 VV3 = 40 V

I1 = 2 AI2 = 2 AI3 = 2 A

IT = 2 A VT = 120 V

RT = 60 AL

R

321 IIIIT

321T RRRR

321T VVVV

Simple Series Circuit

Resistors in Series

12 V

1 2

3

+

2 A

a

b c

d

Voltage Drops Around a Series Circuit

Resistors in Series

2 1 3 12 VI = 2 A

a b c dd

12 V

1 2

3

+

2 A

a

b c

d

Redraw Circuit

Resistors in Series

a b c dd

2 1 3 12 V

12

10

8

6

4

2

0

Voltage DropsI = 2 A

Resistors in Series

Direct-Current Circuits

When two or more resistors are connected in series to a battery

(A) the total voltage across the combination is the algebraic sum of the voltages across the individual resistors.

(B) the same current flows through each resistor.

(C) the equivalent resistance of the combination is equal to the sum of the resistances of each resistor.

(D) all of the given answers 21T III

321T RRRR

321T VVVV

Direct-Current Circuits

As more resistors are added in series to a constant voltage source, the power supplied by the source

(A) increases.

(B) decreases.

(C) does not change.

(D) increases for a time and then starts to decrease.

RV

P2

A parallel connection splits the current; the voltage across each resistor is the same:

Resistors in Parallel

The total current is the sum of the currents across each resistor:

Resistors in Parallel

This gives the reciprocal of the equivalent resistance:

An analogy using water may be helpful in visualizing parallel circuits:

If the pipes have different diameters, then different amounts of water flows through each. However, each has the same drop in height.

Resistors in Parallel

RT = 60

VT = 120 V

IT = 2 A

Parallel Circuit

Cut the resistor in half and

then separate.

Resistors in Parallel

RT = 60 IT = 2 A

VT = 120 V

AL

R

21T R1

R1

R1

21T III

21T VVV

A 1I1 A 1I2 120R1 120R2

V 120V1 V 120V2

Parallel Circuit

Resistors in Parallel

Adding Parallel Resistors Geometrically

Find the equivalent Resistance

60 30

10

20

30

40

50

60

20

Resistors in Parallel

Direct-Current Circuits

Three identical resistors are connected in parallel to a 12-V battery. What is the voltage of any one of the resistors?

(A) 36 V

(B) 12 V

(C) 4 V

(D) zero

21T VVV

Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it.

For these circuits we use Kirchhoff’s rules.

Some circuits cannot be broken down into series and parallel connections.

At junction - a

213 III

Kirchhoff’s Rules and Complex DC Circuits

Direct Current Circuits

Which diagram shows correct current direction in a segment of an electric circuit?

(A) (B) (C) (D)

Review of Chapter

Equivalent resistance of resistors in series:

Inverse of the equivalent resistance of resistors in parallel: