Fundamentals of Electric Circuits Lecture 5 Voltage Dividers, Current Dividers

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 resistance So IR = I(R1+R2+R3) Dividing each side by I R = R1+R2+R3

RESISTORS IN PARALLEL (Review) By Kirchoff’s FIRST law V  I = I1 + I2 + I3 I I1 R1 We now apply Ohm’s Law to each component and to the whole circuit, letting R = the total resistance I2 R2 I3 R3 DIVIDING EACH SIDE BY V

Resistors in series share the same current Voltage Divider Rule Resistors in series share the same current

Resistors in series share the same current Voltage Divider Rule 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 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.

Determine the voltage V1 for the network of fig. Voltage Divider Rule – Example1 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 + V1 - 20Ω 60Ω R2 R1 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’

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

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

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

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

Current Divider Rule (CDR)

Current Divider Rule (Example)

Current Divider Rule All resistors in parallel share the same voltage

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

Current Division All resistors in parallel share the same voltage

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.

Ideal Voltage Source 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 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.

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.

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

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.