CHEM 3420/7420G
Instrumental Analysis
!
Prof. Brian Gibney
2411 Ingersoll
bgibney@brooklyn.cuny.edu
(718) 951 5600 x6636
http://www.hemeprotein.info/Chem3420/Chem3420.php
Chapter 2: Electrical Components
and Circuits
Laws of Electricity
DC Circuits
AC Circuits
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Chapter 2: Electricity Laws
Ohm’s Law
- relates voltage, resistance and current
in a series circuit
V = IR
where
V = potential difference in Volts
I = current in Amps
R = resistance in Ohms
Chapter 2: Electricity Laws
Current is measured in Amperes (Amps)
def. the constant current that produces an
attractive force of 2 x 10-7 newton per meter of
length between two parallel conductors of infinite
length and negligible cross section placed 1m apart in
a vacuum 1 amp = 6.2150948 x 108 e- worth of charge per sec
1 mole of e- has 96,485 Coulombs of charge
(Faraday’s Constant)
2
Chapter 2: Electricity Laws
Potential is measured in Volts
V = J/C Joule per Coulomb
Joule = energy = Newton x meter
Coulomb = current = Amp x sec
= N m / A s
= kg m2 / A s3
Chapter 2: Electricity Laws
Resistance is measured in Ohms
R = Ohms (Ω)
Ω = V/A = m2 kg / A2 s3 Superconductor = 0 Ω Metals
= 10-8 Ω
Copper wire = 0.2 to 40 Ω per 1000-ft
Insulators = 1016 Ω
3
Chapter 2: Electricity Laws
Power Law
- relates power, voltage, and current across a resistor
P = IV = I(IR) = I2R
where
P = power in Watts
I = current in Amperes
V = potential difference in Volts
Chapter 2: Electricity Laws
Kirchhoff’s Laws
- First Law
• the algebraic sum of the currents around any point in a circuit is zero
(there is only one current)
- Second Law
• the algebraic sum of the voltages
around a closed electrical loop is zero
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Chapter 2: Series Circuits
Resistors in Series:
the voltage divider
Chapter 2: Series Circuits
Resistors in Series:
the voltage divider
The current is the same
throughout the circuit
Resistance/voltage vary
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Chapter 2: Series Circuits
Experiment B-2b (p15)
R1 = 100 Ω
R2 = 200 Ω
R3 = 300 Ω
What are ?
V = V1 = V2 = V3 = Chapter 2: Series Circuits
From Ohm’s Law
V1=I1R1
Kirchhoff’s First Law
V1=I1R1 =IR1
Kirchhoff’s Second Law
V1/V = IR1/I(R1+R2+R3)
V1/V = R1/R
A voltage divider
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Chapter 2: Series Circuits
Variable resistance
Potentiometer
Two types selector
continuously variable
Chapter 2: Series Circuits
Just as in any series circuit,the voltage drop
is proportional to the fraction of the total resistance
Top: V/VA,B = (R1+R2)/RA,B
Bottom: VA,C = VA,Bx(RA,C/RA,B)
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Chapter 2: Series Circuits
Experiment B-3a
R1 = 5.1 kΩ
R2 = variable
R3 = 5.1 kΩ
Chapter 2: Parallel Circuits
Parallel Circuits
Current Kirchhoff’s Law
It = I1 + I2 + I3
Current across each resistor is different
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Chapter 2: Parallel Circuits
Parallel Circuits
Voltage Kirchhoff’s Law
V - I1R1 = 0 or V = I1R1
V - I2R2 = 0 or V = I2R2
V – I3R3 = 0 or V = I3R3
Voltage
across each resistor constant
Chapter 2: Parallel Circuits
Parallel Circuits
It = I1 + I2 + I3
and
V = I1R1 or I1= V/R1
V = I2R2 or I2= V/R2
V = I3R3 or I3= V/R3
so
It = V/Rp = V/R1 + V/R2 + V/R3 and 1/Rp = 1/R1 + 1/R2 + 1/R3
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Chapter 2: Parallel Circuits
A pair of Parallel Resistors VB = V1 = V2
and
1/Rp = 1/R1 + 1/R2 or Rp = R1R2/(R1+R2)
Chapter 2: Parallel Circuits
A pair of Parallel Resistors I1/It = (VB/R1)/(VB/Rp) or
I1/It = (1/R1)/(1/R1+1/R2)
or
I1/It = (R2)/(R1+R2) and I2/It = (R1)/(R1+R2) This circuit is a current divider or current splitter
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Chapter 2: Parallel Circuits
A pair of Parallel Resistors I2/It = (R1)/(R1+R2) 1/Rt = 1/R1 + 1/R2
VB = V1 = V2
This circuit is a current divider or current splitter
Chapter 2: Serial Circuits
A pair of Serial Resistors It = I1 = I1
Rt = R1 + R2
V1/VB = R1/(R1+R2)
This circuit is a voltage divider
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Chapter 2: Series-Parallel Circuits
Series-Parallel Circuits
How do we solve for I, V,
and R in these circuits? Chapter 2: Series-Parallel Circuits
Series-Parallel Circuits
Solve for equivalent
resistance
1/Re1,2 = 1/R1 + 1/R2
1/Re1,2 = 1/100Ω + 1/250Ω
Re1,2 = 71.4Ω
1/Re3,4 = 1/350Ω + 1/200Ω
Re3,4 = 127.3Ω
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Chapter 2: Series-Parallel Circuits
Reduce serial-parallel to a serial circuit
R1 = Re1,2 = = 71.4Ω
R2 = Re3,4 = 127.3Ω
Voltage drops
Vt = 24V
V1/Vt = R1/(R1+R2)
V1 = (24V) 71.4Ω / (71.4Ω+127.3Ω)
= 8.62V
V2= 15.38 V = (24V) 127.3Ω / (71.4Ω+127.3Ω)
Chapter 2: DMM
Digital Multimeters
measure V, I, and R
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Chapter 2: DMM
Voltage
measured using high Ω resistor
Loading error
Er = -[(RS)/(RM +RS)] x 100%
Chapter 2: DMM
Current
measured using a standard resistor
Loading error
Er = [(Rstd)/(RL + Rstd)] x 100%
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Chapter 2: DMM
Resistance
measured using constant current source
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