Fundamentals of Electric Circuits

Lecture 5

Voltage Dividers, Current Dividers

2

RESISTORS IN SERIES (Review)

IR1 R2 R3

V

By Kirchhoff’s law (KVL)V= IR1 + IR2 + IR3

= I(R1+R2+R3)If we apply Ohm’s Law to the whole circuit, we have V = IR, if R is the total resistance

So IR = I(R1+R2+R3)

Dividing each side by I R = R1+R2+R3

3

RESISTORS IN PARALLEL (Review)

R1

R2

R3

V

I I1

I2

I3

By Kirchoff’s FIRST law

I = I1 + I2 + I3

We now apply Ohm’s Law to

each component and to the whole

circuit, letting R = the total resistance

321 RV

RV

RV

RV

DIVIDING EACH SIDE BY V321

1111

RRRR

4

Voltage Divider Rule

Resistors in series share the same current

5

Resistors in series share the same current

RT = R1 + R2

Applying Ohm’s law

I = Vin / RT

V1 = IR1 = (Vin / RT) R1

= (R1 / RT ) Vin

V2 = IR2 = (Vin / RT) R2

= (R2 / RT ) Vin

+

V1-

+V2_

Vin

Voltage Divider Rule

6

The voltage associated with one resistor Rn in a chain of multiple resistors in series is:

or

where Vtotal is the total of the voltages applied across the resistors.

totaleq

nn V

R

RV

totalS

ss

nn V

R

RV

1

Voltage Divider Rule

7

Determine the voltage V1 for the network of fig.

V1 = R1(Vin) / RT

= R1(Vin) / (R1 + R2)

= (20 Ω)(64 V) / (20 Ω + 60 Ω)

= 1280 / 80 = 16 V

Voltage Divider Rule – Example1

+ V1 - 20Ω

60Ω

R2R1

Vin 64 V

Voltage Divider Rule –Example 2

Using the voltage divider rule, determine the voltage V1 and V3 for the series circuit

+

Vin

-

R1

R2

R3

45V

2 kΩ

5 kΩ

8 kΩ

+V1

-

+V3

-

+

V’

-

V

V

kkk

Vk

R

VRV

VV

k

Vk

kkk

Vk

R

VRV

T

in

T

in

2415

360

1015

)45)(108(

852

)45)(8(

615

90

1015

)45)(102(

15

)45)(2(

852

)45)(2(

3

33

3

3

3

11

9

Example 3

Find the V1, the voltage across R1, and V2, the voltage across R2.

10

Example 3

Voltage across R1 is:

Voltage across R2 is:

Check: V1 + V2 should equal Vin

+

V1-

+V2_

tVV

tVkkkV

VRRRV

tVV

tVkkkV

VRRRV

in

in

377sin4.11

377sin20 434

377sin57.8

377sin20( 433

)( )(

2

2

2122

1

1

2111

8.57 sin(377t)V + 11.4 sin(377t) = 20 sin(377t) V

11

+V1 -

+V2 -

+V3 -

Example 4

Find the voltages listed in the circuit to the right.

12

Example 5

Check: V1 + V2 + V3 = 1V

VV

VV

VV

VV

VV

VV

R

R

eq

eq

143.0

1 700/100

571.0

1 700/400

286.0

1 700/200

700

100400200

3

3

2

2

1

1

+V1 -

+V2 -

+V3 -

Current Divider Rule (CDR)

Current Divider Rule (Example)

15

Current Divider Rule

All resistors in parallel share the same voltage

16

All resistors in parallel share the same voltage

From Kirchoff’s Current Law and Ohm’s Law :

33

22

11

3210

RIV

RIV

RIV

IIII

in

in

in

in

Current Division

17

All resistors in parallel share the same voltage

in

in

in

IRRR

RRI

IRRR

RRI

IRRR

RRI

213

213

312

312

321

321

Current Division

Ideal Voltage Source Ideal Voltage Source: • The symbol of an ideal voltage source is shown below. The

value of the voltage source is V volts and the terminals “a” and “b” are used to connect the ideal voltage source to other circuit elements.

When any load is connected across the terminals of an ideal voltage source of voltage V, the same voltage V appears across the load, irrespective of the load. Note that the (+) and (-) polarities of the voltage V are on the same side.

Example 1: Various resistive loads are connected to the 5 V ideal voltage source as shown in figure. In each case, the voltage across the load is also 5 V. Note that the equivalent resistance of the resistive load shown in circuit (c) and circuit (d) is considered to be the load.

Ideal Voltage Source

Example 2: Calculate the current I in the following circuit:

Ideal Voltage Source

Ideal Current Source: • The symbol of an ideal current source is shown below. The

value of the current source is I amperes and the terminals “a” and “b” are used to connect the ideal current source to other circuit elements.

• When any load is connected across the terminals of an ideal current source of current I, the same current I flows through the load, irrespective of the load.

Ideal Current Source

Ideal Current Source

Example 3: The 3 A ideal current source shown below is connected to different resistive loads. In each case, the current that flows across the load is also 3 A. Note that in circuit (c), the current through the resistive load is 3 A, but the currents that flow into the individual resistances that make up the load are each less than 3 A.

Example 4: In the following circuit, calculate the voltage V across the 20 Ω resistance.

Ideal Current Source

Dependent Sources Dependent Voltage source: A voltage source whose voltage depends on another voltage or

current is called a dependent voltage source.

Dependent Current source: A current source whose current depends on another

voltage or current is called a dependent current source.