ECE 221Electric Circuit Analysis I
Chapter 4Circuit Elements
Herbert G. Mayer, PSU & CCUTStatus 1/1/2015
Taken with permission from PSU Prof. Phillip Wong
3
Resistor
A resistor is a passive electronic component that obeys Ohm’s Law. It has resistance R
SI Unit: ohm () Symbol: Impedance:
I-V relationship:
R
i(t)v(t)
)()( tiRtv
)(1
)( tvR
ti
RZ
5
Resistors Connected in Series (end-to-end)
If N resistors are connected in series, with thei-th resistor having a resistance Ri , then the equivalent resistance Req is:
N
iiRR
1eq
R1 R2 Req = R1 + R2
Req = R1 + R2 + R3R1 R2 R3
6
Properties of Series Resistances (DC):
The amount of current Iin entering one end of a series circuit is equal to the amount of current Iout leaving the other end.
The current is the same through each resistor in the series and is equal to Iin.
Iin = Iout = I1 = I2 = I3
→ I1
Iin →→ I2
→ I3
→ Iout
R1 R2 R3
7
The amount of voltage drop across each resistor in a series circuit is given by Ohm’s Law.
V1 = IR1 , V2 = IR2 , V3= IR3
By convention, the resistor terminal that the current enters is labeled “+”, and the terminal the current exits is labeled “–”
+ –
V1
I → → I+ –
V2
+ –
V3
R1 R2 R3
8
Example: 2 6 3
A B I
VAB = 3 V
a) Calculate the current I that flows through the resistors.
b) Find the voltage drop across the 6 resistor.
Assume 3 significant figures.Solution:
a) Approach – Use Ohm’s law:
11362eqRCalculate the equivalent resistance:
eq
AB
R
VI
Calculate the current: A273.011
V3
I
b) Use Ohm’s law again: V64.16A273.066 IRV
9
Resistors Connected in Parallel (side-by-side)
If N resistors are in parallel, with the i-th resistor having a resistance Ri , then the equivalent resistance is:
21
21
1
21eq
11
RR
RR
RRR
R1 R2
1
321eq
111
RRRRR3R1 R2
1
1eq
1
N
i iRR
10
Properties of Parallel Resistances (DC):
The amount of current Iin entering one end of a parallel circuit is equal to the amount of current Iout leaving the other end
For parallel resistors, the voltage drop across each resistor is the same
Iin = Iout and V1 = V2 = V3
Iin → → Iout
+ V1 –
R3
R1
R2
+ V2 –
+ V3 –
11
The amount of current through each resistor in a parallel circuit is given by Ohm’s Law.
The sum of the currents through each resistor is equal to the original amount of current entering or leaving the parallel circuit
I1 + I2 + I3 = I
I → → I
+ V –
R3
R1
R2
+ V –
+ V –
I1
I2
I3
I1 = V / R1
I2 = V / R2
I3 = V / R3
12
Example: 2
6
3
A B
I = 4 A
VAB
a) Find the current Ix through the 2 resistor.
b) What is the power dissipated by the 3 resistor?
Assume 3 significant figures.
Solution:
a) Approach – Use Ohm’s law:
13
1
6
1
2
11
eqRCalculate the equivalent resistance:
eqAB IRV
Calculate the voltage drop: V41A4 ABV
b) Use power equation: W33.53
2
ABVP
Find the current: A00.22x
ABVI
Ix
13
Inductor & Capacitor
An inductor is a passive component that stores energy within a magnetic field. It has inductance L
SI unit: henry (H) Impedance:
Symbol:
A capacitor is a passive component that stores energy within an electric field. It has capacitance C
SI unit: farad (F) Impedance:
Symbol: non-polarized polarized+
LjZ
1 CjZ
14
DC Voltage & Current Sources
+–Vs
I
+
–Vs
I
An ideal DC current source outputs a constant current regardless of the amount of voltage across it
An ideal DC voltage source outputs a constant voltage regardless of the amount of current through it
Is V
15
Voltage & Current Dividers
021
22
021
11
VRR
RV
VRR
RV
Voltage Divider
R2
I
R1
+ –
+
–
+
–
V0
V1
V2
IRR
RII
GG
GI
IRR
RII
GG
GI
21
12
21
22
21
21
21
11
Current Divider
I
+
–
VS G2G1
I1 I2
16
Example:
What is the voltage drop across Ra?
What is the voltage drop across Rb?
Sba
bb V
RR
RV
Vb
Ra = 1 Ω Va
+–Vs = 8 V
Sba
aa V
RR
RV
Rb = 3 Ω
V2V831
1
aV
V6V831
3
aV
17
Example:The voltage Vg from a signal generator must be reduced by a factor of three before entering an audio amplifier. Determine the resistor values of a voltage divider that performs this task
3g
out
VV 21 2RR 2123 RRR gV
RR
R
21
2
R2
R1
Vg VoutSignal
GeneratorAudio
Amplifier
Peak output = 3 V Max input = 1 V
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