Presentation on theme: "Fundamentals of Electric Circuits"— Presentation transcript:
1 Fundamentals of Electric Circuits Lecture 5Voltage Dividers, Current Dividers
2 RESISTORS IN SERIES (Review) V= IR1 + IR2 + IR3= I(R1+R2+R3)By Kirchhoff’s law (KVL)If we apply Ohm’s Law to the whole circuit, we have V = IR, if R is the total resistanceSo IR = I(R1+R2+R3)Dividing each side by IR = R1+R2+R3
3 RESISTORS IN PARALLEL (Review) By Kirchoff’s FIRST lawV I = I1 + I2 + I3II1R1We now apply Ohm’s Law toeach component and to the wholecircuit, letting R = the total resistanceI2R2I3R3DIVIDING EACH SIDE BY V
4 Resistors in series share the same current Voltage Divider RuleResistors in series share the same current
5 Resistors in series share the same current Voltage Divider RuleResistors in series share the same currentRT = R1 + R2Applying Ohm’s lawI = Vin / RTV1 = IR1 = (Vin / RT) R1= (R1 / RT ) VinV2 = IR2 = (Vin / RT) R2= (R2 / RT ) Vin+V1-V2_Vin
6 Voltage Divider RuleThe voltage associated with one resistor Rn in a chain of multiple resistors in series is:orwhere Vtotal is the total of the voltages applied across the resistors.
7 Determine the voltage V1 for the network of fig. Voltage Divider Rule – Example1Determine 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+ V1 -20Ω60ΩR2R1Vin64 V
8 Voltage Divider Rule –Example 2 Using the voltage divider rule, determine the voltage V1 and V3 for the series circuit+Vin-R1R2R345V2 kΩ5 kΩ8 kΩV1V3V’
9 Example 3Find the V1, the voltage across R1, and V2, the voltage across R2.
10 Example 3 + V1 - V2 _ Voltage across R1 is: Voltage across R2 is: Check: V1 + V2 should equal Vin+V1-V2_8.57 sin(377t)V sin(377t) = 20 sin(377t) V
11 Find the voltages listed in the circuit to the right. Example 4+V1-V2V3Find the voltages listed in thecircuit to the right.
15 Current Divider RuleAll resistors in parallel share the same voltage
16 From Kirchoff’s Current Law and Ohm’s Law : Current DivisionAll resistors in parallel share the same voltageFrom Kirchoff’s Current Law and Ohm’s Law :
17 Current DivisionAll resistors in parallel share the same voltage
18 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.
19 Ideal Voltage SourceExample 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.
20 Ideal Voltage SourceExample 2: Calculate the current I in the following circuit:
21 Ideal Current 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.
22 Ideal Current SourceExample 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.
23 Ideal Current SourceExample 4: In the following circuit, calculate the voltage V across the 20 Ω resistance.
24 Dependent SourcesDependent 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.
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