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Fundamentals of Electric Circuits Lecture 5 Voltage Dividers, Current Dividers

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2 RESISTORS IN SERIES (Review) I R1R1 R2R2 R3R3 V By Kirchhoff’s law (KVL) V= IR 1 + IR 2 + IR 3 = I(R 1 +R 2 +R 3 ) If we apply Ohm’s Law to the whole circuit, we have V = IR, if R is the total resistance So IR = I(R 1 +R 2 +R 3 ) Dividing each side by I R = R 1 +R 2 +R 3

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3 RESISTORS IN PARALLEL (Review) R1R1 R2R2 R3R3 VV I I1I1 I2I2 I3I3 By Kirchoff’s FIRST law I = I1 I1 + I2 I2 + I3I3 We now apply Ohm’s Law to each component and to the whole circuit, letting R = the total resistance DIVIDING EACH SIDE BY V

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4 Voltage Divider Rule Resistors in series share the same current

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5 R T = R 1 + R 2 Applying Ohm’s law I = V in / R T V 1 = IR 1 = (V in / R T ) R 1 = (R 1 / R T ) V in V 2 = IR 2 = (V in / R T ) R 2 = (R 2 / R T ) V in + V1 - + V2 _ V in Voltage Divider Rule

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6 The voltage associated with one resistor R n in a chain of multiple resistors in series is: or where V total is the total of the voltages applied across the resistors. Voltage Divider Rule

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7 Determine the voltage V 1 for the network of fig. V1 = R1(V in ) / RT = R1(V in ) / (R1 + R2) = (20 Ω)(64 V) / (20 Ω + 60 Ω) = 1280 / 80 = 16 V Voltage Divider Rule – Example1 + V Ω 60Ω R2R1 V in 64 V

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Voltage Divider Rule – Example 2 Using the voltage divider rule, determine the voltage V 1 and V 3 for the series circuit + Vin - R1 R2 R3 45V 2 kΩ 5 kΩ 8 kΩ +V1-+V1- +V3-+V3- + V’ -

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9 Example 3 ¤Find the V1, the voltage across R1, and V2, the voltage across R2.

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10 Example 3 ¤Voltage across R1 is: ¤Voltage across R2 is: ¤Check: V1 + V2 should equal V in + V1 - + V2 _ 8.57 sin(377t)V sin(377t) = 20 sin(377t) V

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11 + V1 - + V2 - + V3 - Example 4 ¤Find the voltages listed in the circuit to the right.

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12 Example 5 Check: V1 + V2 + V3 = 1V + V1 - + V2 - + V3 -

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Current Divider Rule (CDR)

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Current Divider Rule (Example)

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15 Current Divider Rule All resistors in parallel share the same voltage

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16 All resistors in parallel share the same voltage From Kirchoff’s Current Law and Ohm’s Law : Current Division

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17 All resistors in parallel share the same voltage Current Division

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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.

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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

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Example 2: Calculate the current I in the following circuit: Ideal Voltage Source

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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

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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.

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

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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.

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